Mr. Alexander, "king of the window dressers" at Hawthorne's chic department store, is busily preparing a lingerie window, pulling down the window shades to prevent a passer-by's prying eyes from watching his work. He calls the mannequins by name and talks to them, chastising their "behavior". One particular mannequin has moved from her correct position. When Mr. Alexander shifts the mannequin, a man's body falls out from behind. Mr. Alexander screams and runs right through the plate glass window onto the street. A car parked nearby suddenly takes off with a squeal of tires.
Miss Larchmont, representative of Intimate Airlines, is helping Burke prepare for his upcoming trip to the police convention in Chicago, where is to give a speech. She "sells" the airline's special services, carrying Burke's luggage and telling him that he is her "personal" responsibility. Miss Larchmont administers the "Intimate Airlines Oath" to Burke, where he swears to have a good time. When the call comes about the murder, he turns the case over to Tim and Les and heads off to Chicago.
The dead man is one Arthur Colby, a maintenance man at the store. He has been struck on the head with one of his own hammers, and had $680 in his pocket. Tim and Les hope to tie up the case before Burke returns. They interview Mr. Alexander, who is now calmer and perturbed that a body should be placed in "his" window. He tells them he was fleeing and couldn't identify the car.
After being shunted from one assistant to another, Les finally interviews Denise Mitchell, the owners' friendly executive assistant. She tells him that there are two Mr. Hawthorne's. Mr. H, Sr. is currently in Europe and Mr. H, Jr. never gets in to work this early. When she goes to retrieve Colby's personnel records, the files are missing. Ms. Mitchell can't understand how this could be, since only senior executives are allowed near the files. She tells Les that Colby was a quiet man and calls maintenance to get his address. She also gives Les "Junior's" address, an entire city block.
Tim pulls up to the store in Burke's car, Les throws him out and tells him to check out Colby's home. Then Les gets in the car and tells Henry to drive him to Hawthorne, Jr.'s address (it would never do to show up in a squad car).
At the Hawthorne estate, Guy Jr. sits poolside, drinking, while his elderly butler, Smithers, on a stationary bike, and elderly chauffeur, Coates, on a rowing machine, exercise for him. The rest of the estate is a faux jungle. Guy Jr. is covered from head to foot, since the sun is bad for him. He tells Les this form of exercise is "mind transference" - you hire someone to do what wears you down. He says he seldom goes to the store (just to please the pater), doesn't like being "in trade", and didn't know Colby. Colby was hired on the recommendation of Maggie French, head of the store's high fashion section. Guy Jr. says she will be returning from an out-of-town buying trip later that day. He ends "his" exercise and orders the servants to jump (fully clothed) into the pool, so he won't stiffen up.
At Colby's address, Tim interviews sidewalk hawker/pitchman Ernie Webb. Webb says he's never heard of Arthur Colby and has lived there, alone, for three years. He tells Tim all about the hard life of a pitchman, either on the sidewalks or in the burlesque houses ("If I never see another zipper..."). Tim finally buys one of his windup toys.
The next day, Mr. Alexander doesn't show up for work and doesn't answer his phone. This has never happened before, and there's a window to be finished. At his apartment, Mr. Morrow the supervisor, lets Tim and Les in to look around, but they find nothing. Just as they leave, Mr. Alexander walks in and drops dead in the doorway. He has been poisoned with lead arsenic, probably in a drink. The M.E. also reports that there is no good print on the hammer used to kill Colby. Sgt. Ames sneakily hums "Chicago", suggesting they call Burke, but Les and Tim refuse. They try to figure out Colby's real address, Les suggesting they try by tracking banks where he cashed his paycheck, Tim thinking of checking with the union. Les goes off to check, sending Tim to Hawthorne's fashion show.
The fashion show is only for male buyers. Maggie French tells Angela, a non-too-bright model, how to best sell a sexy nightie. She tells Tim the only way to sell is - husbands, champagne and girls. She says Colby was just a nice fellow she tried to help; she met him at the races. Maggie races cars as therapy from her job.
Sgt. Ames is furious that the dinner she prepared is being ruined because Les hasn't shown up. Burke calls them from Chicago. Tim pretends everything is OK with the case. Burke says he's snowed in a won't be back as soon as he thought.
DUTY WILL ALWAYS INTERRUPT PLEASURE - BURKE'S LAW
Burke is actually "snowed in" with a lovely brunette, rehearsing his speech.
Les shows up, having gotten Colby's social security number through the check-cashing place where he always cashed his paycheck. His real name is Al Cole,he has a long criminal record of crimes against women (extortion, bunco, etc.), and he's still wanted in three cities. From this Les gets Colby/Cole's real address. He and Tim leave Sgt. Ames with a ruined dinner.
At Cole's apartment, much too fancy to be paid for on a janitor's salary, they interview the manager, Mr. Fitzell. He tells them Cole liked to entertain a lot of ladies. They find two glasses on the bar, one with lipstick traces. Tim finds a little key, like the one used to wind up Ernie Webb's toys.
At Webb's home, they confront him as he comes from work, looking askance at his garage. They make him open the locked garage door, discovering box after box of merchandise stolen from Hawthorne's. He tries to run and Tim socks him. At the station, Webb insists they only have him on possession charges. He says Cole conned him into accepting stolen merchandise. Webb says he wanted to stop, but Cole would have stolen the whole department store building if he could. Webb told him his nerves were shot, and Cole claimed he had protection from a woman in the store. Webb says he was afraid of Cole.
Tim goes to confront Maggie at the racetrack. She says she was married to Cole 8 years ago, when she was a nobody. She put up with his temper for a year, then got a divorce. Cole only liked money and racing. When he came to Hawthorne's, he apologized and "asked" her to do him a favor (or he'd tell Hawthorne Sr. about her past - she'd been taking sleeping pills because of their fights and crashed her car one night). Maggie knew she would have been dropped from the store, so she helped him get his job.
The car that sped away from the crime scene was ticketed by a passing cop that night. Tim and Les find it belongs to one Davey Karr, currently working as a bus driver on a tour of movie star homes. Sgt. Ames goes to investigate and the man sitting next to her tries to pick her up (she tells him she's a plumber, he says he's got a leak in his room). As the bus passes different homes, Davey does impersonations of the home owners (Cagney, Kirk Douglas). When a woman complains that the house they just passed doesn't belong to Kirk Douglas but to Edd Byrnes, Davey says he knows, but he doesn't "do" Edd Byrnes. At the western lot, as the passengers disembark, Ames shows her badge (which sends the Romeo running) and questions Davey. He says he is a wannabe nightclub comic who was a hit in his home town but can't get work in L.A. He got a job as a busboy in a strip joint and got his big chance on New Year's Eve, but his act bombed. He got in a fight with a customer and hurt him bad. Cole was there and blackmailed him (half his pay from then on). Davey says he went to store to ask Cole to stop, but never worked up enough nerve to go in. He says he's a "nothing comic" and couldn't "kill" anyone - ask the audience.
The prints from the glasses in Cole's apartment are checked, as is a winning daily double ticket Tim discovered - worth $87,000. In Chicago, Burke tells them not to be upset.
YOU SWEAT 'TIL ALL THE PIECES FALL INTO PLACE AND THERE IT IS STARING RIGHT AT YOU - BURKE'S LAW
He realizes that, since Cole had a record, he couldn't claim the winning ticket (IRS and reporters would jump on him). Burke tells them to figure out who knew he had the ticket and says he'll be back tomorrow, then goes back to his lovely brunette. Just then, Sgt. Ames comes in with the lab reports. The woman in Cole's apartment was Denise Mitchell.
Denise tells Les she always picks the wrong man; she fell for Cole the day he applied for the job (she was on the rebound from another bad affair). She would never have killed him because she was in love with him. Denise says she knows nothing about a winning ticket, but new Cole was excited about something involving money. She tells Les the last "wrong man" she was with was Guy Jr. Guy Sr. was a total tyrant who made everyone jump and kept his 41-year old son on a tight rein, forcing him to live on a small allowance.
In the Rolls, Tim and Les mull over the case and realize there's only one conclusion and one way to deal with it. Les tells Tim
IF IT LOOKS RIGHT, JUMP; DON'T JUST SIT THERE
Tim says "BURKE'S LAW?" and Les replies "You know it!"
In the estate "jungle", Tim meets with Guy Jr, who's training a toucan. Tim pretends to be a track ticket seller who has the winning ticket and saw Guy Jr. behind Cole in line at the ticket window. He offers to "split" the money with Guy (he can't cash the ticket as an employee). When Tim shows Guy the ticket, Guy pulls a gun and says he'll have it all. Mr. Alexander had realized that Guy was in the store "working late" that night and had tried to blackmail him, so he killed him as well. Tim "drops" the ticket, throwing Guy off guard. Tim hits Guy and Guy runs off, firing the gun behind him as Tim (and Les as well) give chase. Tim jumps Guy and they fall into the "jungle lagoon". Tim subdues him. As Guy is behind led off, he comments on the irony of Mr. Alexander's blackmail - he was 41 and totally broke. Tim realizes the winning ticket is in his pocket, soaking wet and turning to mush.
Les, Tim, Sgt. Ames and Henry prepare a huge party to welcome Burke back. Miss Larchmont drives him into the living room in her little airport motorcart and gives him a farewell kiss, as part of the service of Intimate Airlines.