A woman is kidnapped. While in captivity, she manages to send a message out with a wandering cat. The cat's owner calls the FBI. The FBI tries to follow the cat. Jealous boyfriends and nosy neighbours also get in the act.
Two sisters, Ingrid and Patti Randall, are temporarily alone in their suburban home with "That Darn Cat," nicknamed DC. At night, DC roams free, courting a female cat and following Iggy, who carries a piece of salmon. Iggy and Dan, two bank robbers, are holding Margaret Miller hostage while hiding from the police. Iggy decides to let DC in and feed him; and while DC is in the apartment, Margaret takes off his collar and substitutes her watch scratched with the word "Help." At the Randalls, Patti spends the evening with her boyfriend, Canoe, and Ingrid accepts a dinner invitation from Gregory Benson, an accountant whom she does not like. When DC steals the dinner, Gregory threatens to shoot him. Patti finds Margaret's watch and wants to call the police, but Ingrid forbids it, so Patti calls the FBI. Supervisor Newton assigns Zeke Kelso to the case, and Kelso assigns three agents to tail DC, but the cat eludes them. Meanwhile, all the action at the Randall house is watched by Mrs. MacDougall, a snoopy neighbor. With a bugging device implanted in his collar, DC leads Zeke into a chase at a drive-in movie and through Gregory's backyard, where Gregory shoots at them. Later Gregory finds Ingrid and Zeke alone together and breaks up with Ingrid. On the third night of being tailed, DC is followed by Zeke, Patti, Canoe, and Mrs. MacDougall. Patti and Zeke rescue Margaret, and the next day DC visits his mate and their new litter of kittens.
