At the tail end of a jet-set party in a hotel bungalow, Burke is singing "C'est Si Bon" to the remaining drunken crew, especially a sexy brunette on the sofa. During the song, the doorbell rings, but no one is there when he answers, still singing. Suddenly a shot rings out and he falls back into the room next to the brunette, who screams when she realizes that he's dead.
Tim and Les supervise the crime scene, when suddenly Burke walks into the room. The dead man is actually Snookie Martinelli, international playboy. Tim and Les insist that Burke look at the body. He merely comments on the gunshot wounds. They insist that the dead man looks just like Burke. Burke looks again and says the man is grayer, heavier, jowlier and older - much older. Les tells Burke Martinelli is all part of a jet set crowd staying at the hotel, and their next destination is Paris. The person next door, Seraphim Parks, phoned in the shooting. Tim gives Burke a lesson on angel hierarchy, with seraphim the highest. Just then the brunette who screamed walks back into the room, looks briefly and disinterestedly at Burke and says "you're new". She then cozies up to Tim. Les comments that she must like them younger. Burke winces and comments that she obviously didn't think he looked like Snookie.
When he knocks on the door of the next bungalow a woman calls out "it's always open". When he enters, he finds a trail of discarded clothing, shoes, dress, stockings, ending with Serpahim, nude in bed, brushing her hair. She immediately notices the resemblance to Snookie and complains Burke made her lose count when he asks if she killed Snookie (she brushes her hair 200 strokes every night). Burke says he'll keep track of the count if she'll give him info on the party guests. She tells him that Binky Fawcett left early ("the party pooper") after a spat with Snookie. She says everyone at the party is at the hotel. Burke keeps her passport. When asked why she's named Seraphim, she replies "My mother was an optimist". She tells Burke she adored Snookie. Seraphim tells Burke she doesn't remember exactly what she was doing when at the party, that as usual she just "floated" all evening. She suggest that he go out with her to a club to hear a band. Burke turns her down and she pouts.
When Burke enters the station the next day, each person he meets asks if he's seen the morning papers. Finally he looks and sees a huge picture of himself/Snookie on the front page. It's big news, but Burke still thinks Snookie looks older. Snookie was shot with a .32 and one footprint was found alongside the walk near the bungalow (When asked, Tim has already had a cast made). Les comments that the guilty party will certainly be shocked when they see Burke walk in.
When Burke enters Binky's suite, Binky immediately gasps and runs, heading for a chest of drawers. Burke pulls a gun, but Binky is only going for a beret to cover his bald head. He apologizes and says he wasn't covered. Burke indicates his gun and says "yes, you were". Binky goes to a dressing table and begins selecting which toupees, from a huge collection, he will wear at which part of that day. When he says "never an end to work", Burke agrees and Binky thinks this means that Burke is also wearing a toupee. He comments on how natural it is. His fight with Snookie was about Snookie threatening to drop him from the set because he couldn't "keep up". Binky complains how hard it is being an official hanger-on - he's been Snookie's "house guest" for 11 years. He can't do much else and can't get a foot up because he has the wrong school tie and the army just let him go. He says Snookie had no right to drop him, "after all I've done for him" (protecting him from jealous husbands and lying to his many women), but it just wouldn't be posh to kill someone. Binky laughs when Burke asks if he noticed the resemblance, and tells Burke that Snookie was handsome, younger and much taller than Burke. When Burke insists on knowing why he was cashiered from the army, Binky says he was "naughty" and killed a man.
Tim and Les question jet-set member Louis Simone, speedcar racer, during a pit stop, but he insists he can't talk to them until after the race. Right after that, he spins out on a curve and is eliminated from the race. Later, in the locker room, he just say "C'est la vie". He comments that Snookie knew the important things, like how to love. Snookie was so good he stole Simone's wife, but Americans don't understand that that would be no reason to kill him. Having shared the same wife actually makes him and Snookie brothers. Simone admits that Snookie was smarter, because he got all the money. "But all that was two wives ago" he poo poos. When asked how he fits in, Simone says "I AM the jet set!" and he's the pied piper of the group. He left early because he had picked up a beautiful woman. Simone insists he wouldn't kill Snookie because he was Simone's patron and paid for all his races. Tim comments that owing that much money would be a good excuse. Simone scoffs that Americans think too much about money. He says that if he had killed Snookie he would have done it in Paris because Paris has a nicer atmosphere. He leaves, saying he has a date with an "angel".
Burke enters his home to find Seraphim's castoff shoes and stockings and fur in a trail to the living room. She tells him she had a terrible time getting out of her date with that "awful" Louis Simone and suggests they go out to dine.
ALWAYS TAKE MATERIAL WITNESS TO DINNER - BURKE'S LAW
When Burke tells Henry about going out, Henry is furious because he's just made Hungarian goulash.
When they reach the Chez Charles, Seraphim has already doffed her shoes again. She is still vague about the set, telling Burke again that she "just floats" and has known Snookie since Hong Kong, whenever that was.
Just then the star attraction, pianist Jango Jordan, billed as "Play it Jango", begins his act. Seraphim yells out the standard request "Play it, Jango!" and he begins a mournful tune dedicated to her. She tells Burke how much she loves the tune and that Jango played it the night Snookie died, just before the fight. Burke says she's never mentioned they were at the club or that there was a fight. She shrugs it off and says it was with ex-prize fighter Carlos Varga, who wasn't at the party. Burke says yes, but he knew where the party was. He goes to phone Sgt. Ames to locate Varga and returns to find just Seraphim's shoes. She's now sitting on the piano bench with Jango, an old friend since Rome, Venice and the Riviera, as was Snookie. Jango begins to play and sing "How Little We Know", but warns Burke that putting shoes on the piano is bad luck. He comments on how much Burke looks like Snookie and says it gives him the creeps.
Varga is located at Mr. Jacques salon, getting a pedicure and manicure, with his hair up in curlers under a drier. He warns Burke his nails are still wet and comments on how much style he has. Burke scoffs and Varga comments that as a boxer he was #3. Burke says he was #1 in taking dives. He reminds Varga that he has a record - took a notorious dive when he fought as Mushy O'Toole, had a concealed weapons charge, as well as assault, and was a runner for the syndicate. Varga says he wouldn't kill Snookie because Snookie was his "pet-run" (meaning patron). When pressed, he tells Burke he'll get an alibi. Snookie hired Varga to follow the set around, but Varga fought with him when Snookie told him he had no class. He says Snookie never understood him but his wife, Eva Martinelli did. Her ship is due to dock that day from a voyage to Mexico. As Burke leaves, Varga examines his nail polish.
Burke, Tim and Les go to the dock to meet Eva. An oil heiress, she's Snookie's wife #4 and he's her husband #5. Burke pretends to be Snookie when she comes ashore and she acts as if he is, commenting on how much better he's looking, until Eva finally admits that she knew all along, when Burke pumps her for information. She had received a wire that Snookie was dead. Still, she flirts with Burke when he offers her a ride home, after telling Tim and Les to find out if she could have left the ship. As Burke explains to Eva
NEVER DOUBT A WOMAN FOR THE FIRST FIVE MINUTES - BURKE'S LAW
At Chez Charles, Burke finds Jango, with Seraphim's shoes, playing the same sad tune. Jango gives him his views on the jetset - Binky is pathetic, Seraphim is great, Varga is "always pushing and getting nowhere - they'll drop him and find a new kick soon", Simone loves playing with curves, and Eva plays in the shadows (she doesn't like the light). He says he's glad to have this gig and be rid of them all because they're "malnourished" from living on nothing but whipped cream.
Seraphim comes down the stair of the club, wrapped in a sheet. Jango leaves on his break. Seraphim complains that Burke keeps asking questions, but never the right one. She says "THAT'S NO FUN". Burke replies:
MURDER SELDOM IS.
Seraphim wants to know if that's BURKE'S LAW, too. Burke tries once again to question Seraphim, but gets a call. Tim checked Eva's alibi but all the crew swears she never left the freighter (but then she owns it, so they could all be lying). Burke comments that no one cared enough about Snookie to kill him, but maybe the fact that he resembles Burke is important - maybe Burke was the intended victim and Snookie was mistaken for him. Just then, someone fires at Burke, shattering the mirror he's standing beside. But why does someone want to kill Burke?
Les discovers, by doing some heavy drinking with one of the ship's oilers, that Eva did leave the ship and was unaccounted for when it was laid up in Ensenada for twelve hours.
Burke finds Eva at home in candlelight. She's startled again by the resemblance when he enters. He asks if she wanted to be rid of Snookie. She plays Jango's sad tune and says how much she loves it; it was a love theme from her husband. Eva tells Burke that men always married her for her money. Snookie was different. He loved her at first; then it became about the money, like all the others. The day he died, Snookie wired Eva and she flew to him, but he just wanted more money. She says she could have killed him, but didn't, and was back at the ship when he died. When Burke leaves, she begs him not to leave her alone. He says he won't and leaves a policeman on guard outside her door, after introducing them.
Burke tries out several theories on Henry regarding who was the intended victim and why, but finds fault with all of them. He can't get Jango's song out of his mind. He suddenly thinks of something and tells Henry he'll get a raise if he can get them to Chez Charles in under 10 minutes (Henry does it in 9 minutes and 2 seconds).
At the club, Seraphim has left and Jango is closing up. Burke asks him to play the song and says the club is the only place that Burke and Snookie had in common. He realized that when Eva said the song was a love theme from her husband, she was referring to Jango not Snookie. Jango was her previous husband and Snookie stole her away from him, a great motive for murder. Jango says: IT TAKES MORE THAN MOTIVE FOR MURDER and Burke notes that "you're playing my song" with another BURKE'S LAW. Burke knows that Jango could have gotten to Snookie, killed him and made it back on his 20-minute break. Also, he was on a break when Burke was shot at (done in order to confuse the issue and make Burke think that he was the intended victim all along). Burke tells Jango the footprint will prove his guilt, because, like fingerprints, no two footprints are alike. Jango pulls a gun. He complains that Snookie was like all the other "handsome" jet setters; Jango brought Snookie into the group. Then Snookie stole his wife and turned Jango into a monkey on a stick. He saddled Jango with the curse of "Play it, Jango" which meant Jango was never taken seriously again.
Les and Tim arrive to tell Burke that the footprint belonged to someone else. Jango says it's too late and holds the gun on them as he makes an escape. However, he trips over Seraphim's discarded shoes and falls. Burke says "an angel is looking over us".
Later, in Burke's car, he and Seraphim are drinking champagne out of her shoes. As they embrace, Burke finds a white feather on his shoulder. Is she really an angel? Seraphim just smiles.