Los Angeles police officers Joe Friday(Webb) and Bill Gannon (Morgan) are visited one day by one Charles Porter (Prentiss), a wealthy man who's very concerned about the welfare of his only grandchild, Robin Shipley. Porter's concern rises from the fact that his daughter Jean Shipley (Scott) and her husband, systems analyst Paul (Donnelly) admit to using marijuana.
Friday and Gannon pay a call on the Shipleys at their posh home in the San Fernando Valley. Though Jean refuses a search of the home, she admits that she does in fact smoke marijuana as does Paul, who comes in mid-interview, looking upset. The Shipleys resent the intrusion of Porter and the police, but as there is nothing to arrest them for, Friday and Gannon leave a little frustrated.
Friday and Gannon approach policewoman Dorothy Miller (Anders) who specialises in cases of child abuse. Though Miller is sympathetic, she is loaded down with some very serious cases (including a child who was beaten with an electric cord) and since there is no evidence the Shipleys are abusing Robin, there is nothing she or the others can do.
Time passes and Friday and Gannon get a break. One Fred Ludden (Oliver) is arrested for possession and the two detectives get him to admit he got the marijuana for free from the Shipleys. In short order, the police raid the Shipley home, where a pot party is still in progress. The Shipleys, both high, seem more annoyed than anything else at first, even when Gannon retrieves a bag of reefer (about two pounds). But when Friday notices Robin is missing from her playpen, Paul Shipley can't remember where she is, Jean tries to remember, but is having trouble - then runs fearfully to the bathroom. When she gets there she and the detectives see the bathtub is everflowing, Robin still in there, drowned. Jean and Paul, both heartbroken, break down crying. Gannon has to leave the room to throw up, leaving Friday, still holding the bag of grass, to walk towards the camera, his face out of shot. As the familiar Dragnet theme plays, Friday's hand tightens around the bag in rage.
In the end, Paul Shipley is sentenced to prison on possession and distribution charges. Jean Shipley, apparently driven mad by her grief, is not charged but sent to a mental institution.