On Halloween night, Granny is shopping for candy at a local grocery store. The next customer is an armed robber, who is wearing a blouse and skirt identical to the real Granny. Policemen Daffy and Porky (whose role as a policeman may be a play on "pig" being slang for such) are given the suspect's description and attempt to apprehend the robber.
Most of the rest of the cartoon depicts Daffy and Porky confusing Granny with the actual suspect (because of their identical clothing), and bungling said attempts to capture the crook. An annoyed Granny, who has no idea what is going on, mistakes the inept policemen for mischievous trick-or-treaters and mistakes real trick-or-treaters for juvenile delinquents, while the robber (who is hiding out in a vacant apartment in the same building Granny is living) also foils every attempt by Daffy and Porky.
Eventually, Granny figures out what is going on and catches her "double." After giving the suspect a spanking, she hands him over to Officer Flahrety. Flahrety commends Granny for catching the robber, after which Granny tells him "there are two other juvenile delinquents" who should be sent home to their parents (referring to Daffy and Porky), but when she asks for their addresses, Daffy gives her their precinct address and begs her to back off.
The cartoon marked the final theatrical pairing of Daffy Duck and Porky Pig during the original Golden Age of Animation era, and the only one during the time that Warner Bros. cartoons were being produced by DePatie-Freleng Enterprises. In addition, Granny - voiced here by Joan Gerber instead of June Foray - makes her final appearance, as does Porky during the 1960s. "Corn on the Cop" also reveals Granny's actual last name: Webster (in the closing scene where Daffy and Porky's superior police officer addresses Granny by name).