Abby and Martha Brewster are two “old maid” sisters in their mid-60s who live in a quiet neighborhood in Brooklyn, New York with their nephew Teddy, who believes that he is Theodore Roosevelt. The sisters are kind and well-loved by their neighbors. Early in Act One another nephew – Mortimer Brewster, who is a theater critic – visits his aunts, as he does almost daily, and proposes to his long time girlfriend Elaine, who lives with her father in the house next door. After Elaine goes home to tell her father of her engagement, Mortimer starts looking for some papers he left there earlier and eventually looks in the window seat – where he finds the dead body of an elderly gentleman, Mr. Hoskins. Mortimer at first believes that it is his brother Teddy – who everyone already knows is insane – who killed the man, but Abby and Martha soon tell him that they are the ones who killed him, and then tell him that they have killed 11 other “gentlemen” and had Teddy bury them in the basement; they poisoned each of their victims with arsenic, strychnine, and cyanide mixed in elderberry wine. When asked why, the sisters tell Mortimer that the men were lonely and miserable, and they were doing them a kindness.

Mortimer immediately sets about trying to figure out how to cover up his aunts’ crimes and, although he and Elaine were going to the theater that night to see a play Mortimer was supposed to review, he rudely sends her home and tries to find someone to cover for him. When he is unable to do so, he heads out to the theater alone, after making Abby and Martha promise not to let anyone in the house, and not to have Teddy bury the body until he gets back. A short time after he leaves a knock comes at the front door and even though Abby and Martha pretend they are not home, two men come into the room. One of the men is their nephew Jonathan, who is the black sheep of the family and who has a face that looks like Boris Karloff as the result of a botched plastic surgery that was done by the other man, Dr. Einstein. (Note: In the original stage production, Jonathan was actually played by the actor Boris Karloff.) Jonathan and Einstein are criminals who are on the run and have come to the house in Brooklyn to hide out. Although Abby and Martha try to get rid of them, they end up staying to dinner as the first act ends.

After dinner, Jonathan tells his aunts that he needs a place to stay, and they reluctantly agree that he can stay in his old room for one night. Teddy then takes Dr. Einstein down to the cellar to show him the new “lock” he has dug in the Panama Canal; the “lock” is actually the grave the sisters had him dig for Mr. Hoskins. As Abby and Martha head upstairs to prepare his old room, Dr. Einstein comes back and tells Jonathan that the hole in the cellar will be the perfect place to bury Mr. Spenalzo – a man who gave the two of them a ride, and who Jonathan strangled after he said that his face looked like Boris Karloff’s. They agree to bring the body inside through the window and bury it after everyone has gone to bed, and a few minutes later, they head up to their room to unpack after Jonathan orders Abby and Martha to go to bed. When everyone is upstairs, Teddy comes in and moves the body from the window seat to the cellar. A few minutes later, Jonathan and Einstein come downstairs and bring Mr. Spenalzo in through the window, but are interrupted by Elaine who comes back into the house looking for Abby and Martha. Einstein manages to get Mr. Spenalzo into the now empty window seat before Elaine sees the body.

Mortimer returns from the theater as Elaine is being taken to the cellar by Jonathan, and Elaine runs to his arms. Mortimer orders Jonathan out, but reluctantly agrees that he can stay since his aunts invited him. He then rudely sends Elaine home again, telling her that he can’t marry her because madness runs in the Brewster family. Mortimer, who thinks that Mr. Hoskins is still in the window seat, says that he will sleep downstairs, but Jonathan insists that he and Einstein will sleep downstairs. When he has a moment alone, Mortimer looks in the window seat and sees Mr. Spenalzo in there rather than Mr. Hoskins. When he questions them, Abby and Martha tell him that they have no idea who the man is – that he isn’t one of their gentlemen – and Mortimer understands that this is one of Jonathan’s victims. He tells Jonathan that he knows about the body, and gives his brother one chance to get out, and take Dr. Einstein and Mr. Spenalzo with him. Officer O’Hara then enters because the neighbors have complained about Teddy blowing his bugle and, after he tells Mortimer that he is an aspiring playwright, Mortimer offers to listen to the plot of his play as a way to keep him there until his brother leaves. As he is about to leave, Jonathan sends Dr. Einstein to the cellar to get a case of instruments they stored down there, and Einstein sees the body of Mr. Hoskins in the open grave. He returns and tells Jonathan they don’t have to leave, that they have an “ace in the hole”. Jonathan tells Mortimer what they have found in the basement and asks if O’Hara would like to go down there. Mortimer then leaves with O’Hara to listen to the plot of his play, and Jonathan and Einstein prepare to bury Mr. Spenalzo.

The third act begins with Mortimer returning after ditching Officer O’Hara, just as Jonathan and Dr. Einstein are finishing burying Mr. Spenalzo and Mr. Hoskins in the same grave. Abby and Martha are very upset about this and threaten to go to the police, but Mortimer tells them he will take care of everything, and they head to bed. After Dr. Einstein tries to get Mortimer to leave for his own good, Jonathan sneaks up behind him and ties Mortimer to a chair and gags him, and then makes plans to kill him using the “Melbourne method” – which usually takes two hours – even though Dr. Einstein begs him to use the quick way. As they are about to start, Officer O’Hara comes back into the house because Teddy has blown his bugle again. He sees Mortimer tied and gagged and, rather than releasing him, takes the opportunity to tell him the plot of his play as the curtain comes down. When the curtain comes up again, it is several hours later – early morning – and O’Hara is still telling the bound and gagged Mortimer the plot of his play. Jonathan is asleep on the sofa, and Dr. Einstein is listening seated at the table, drunk.

Two police officers then enter the living room; they have come to arrest Teddy for blowing his bugle during the night. They free Mortimer and arrest Jonathan, who is recognized as being an escapee from a prison for the criminally insane. Elaine then enters with Mr. Witherspoon – the director of the Happy Dale Sanitarium – and it is agreed that Teddy will go there that very day. Abby and Martha are upset by this and after they tell the police that there are 13 bodies buried in the basement (which no one but Mortimer, who knows the truth, believes) Mr. Witherspoon agrees to let them commit themselves to Happy Dale and be with Teddy. Dr. Einstein is allowed to escape after signing the commitment papers for the sisters. Abby and Martha then reveal to Mortimer that he was actually adopted and is not really a Brewster, and he is overjoyed as he realizes that he will not go mad like the rest of the family and can marry Elaine. As the curtain goes down, Abby and Martha are offering Mr. Witherspoon – who has told them that he is lonely and unhappy – a glass of elderberry wine.