After dinner at the Addamses home, Morticia worries that Gomez ate too much of Grandmama's yak stew. Gomez feels sleepy and goes to bed. When Morticia comes in, she discovers that Gomez is fast asleep with a lit cigar in his mouth. She goes to bed but wakes up later and finds Gomez fully dressed and sleepwalking. He goes out to the hallway and Morticia knocks at Fester's door. Fester figures that it's a nice night for sleepwalking and they agree that Gomez should be fine.
The next afternoon, Gomez comes down to the greenhouse as Morticia and Fester feed the plants. He's surprised to learn that he's been asleep for eighteen hours, and doesn't remember anything that happened the previous night. The newsboy delivers the paper and Fester reads a story about how there's a cat burglar in the neighborhood.
That night after dinner, Gomez dozes off again and Morticia realizes that he's eaten too much yak stew again. She worries that her husband will go sleepwalking again and stumble across the cat burglar, and Fester agrees to stay awake and on watch all night. He quickly dozes off outside the bedroom door and even Grandmama setting his ulster on fire fails to wake him up. Or her pouring water on it to put the fire out. Or Lurch walking by and knocking over the chair. The butler props the sleeping Fester back up in his chair and goes back to bed... and Gomez sleepwalks past.
The next afternoon, Morticia is happy that she found Gomez in bed with her when she woke up, even though his shoes were covered in mud. Fester dismisses it as Grandmama's poor housecleaning and finds more newspaper stories about the cat burglar. Gomez comes in and says that he had a dream about walking down the street and through a mud puddle, and discovers that his shoes are covered in mud. While Thing cleans his shoes, Gomez assures Morticia that he wasn't out. Morticia takes Fester to the storeroom, figuring that he dozed off, and they're surprised to discover the room is filled with stolen loot.
Morticia and Fester tell Grandmama and Lurch what they've discovered and figure that Gomez is the cat burglar. Grandmama remembers that Gomez's father sleepwalked after eating yak stew, and they vow to keep Gomez from eating any more stew. Unfortunately, Gomez comes in and says that he ate the rest of the stew in the refrigerator. Once he goes to the library to play with his trains, Morticia suggests that they use hypnosis to delve into Gomez's mind and find out why he's robbing people.
Morticia convinces Gomez to listen to her play the snake charmer's flute and manages to put Fester and Grandmama into a trance. Once they snap out of it, Gomez suggests that he try the same thing with a trumpet and manages to hypnotize himself. Morticia shows him pictures from a book and they all remind him of robbing people. Frustrated, she wonders why everything reminds him of cat burglary, and Gomez says that Robin Hood is his idol and takes out a book about the bandit. When Morticia explains to Fester what she's learned, Fester wonders why Gomez never gives anything to the poor. They check Gomez's book and realize that he's only gotten halfway through it. They hide the book and Morticia starts to give Gomez a command to return the stolen items. However, she says "voila" in France and Gomez comes out of his trance to kiss her arm before she can finish her command.
Lurch and Fester lock Gomez in the storeroom until Morticia can find some chains. However, they discover that Gomez has escaped through the hidden passage. They wait up for him and Gomez comes back at 3 a.m. with more loot and dumps it on the table. Morticia has Lurch dump water on Gomez's head, waking him up, and they tell him what he's been doing. Gomez, shocked, wants to return everything he's stolen but has no memory of who he took it from.
As the family tries to come up with a plan, two police officers pull up outside. Morticia realizes that they won't believe the truth and Gomez hides with the loot. Lurch lets the officers, Rogers and Hix, come inside and they explain that the cat burglar gave them the slip nearby. Gomez comes back in, disguised as an old man, and claims to be Morticia's grandfather Alonzo. The police have a list of all the stolen items and who they belong to, but refuse to let Morticia see it. Morticia speaks French and Gomez gives away who he really is, and the officers remove his disguise. When they try to explain about Gomez's sleepwalking, Morticia plays the flute and the two officers go into a trance. Morticia gives them the loot and a hypnotic command to return everything on the list to the proper owners, and sends them on their way.
The next day, Gomez discovers that his new $5,000 wristwatch is missing. Fester remembers that he gave it to the officers because he thought it was part of the loot, and Gomez tells Grandmama to cook up some yak stew so he can steal it back.