If you can compare the formal method of Perry Mason to a sonnet, "Fade in to Murder" is as simple as a musical phrase. Lt. Columbo's suspect is America's favorite television detective, Detective Lucerne. The actor playing him is a Korean War deserter who has been paying blackmail to the show's producer, and finally kills her. Lt. and Mrs. Columbo are great fans of the show, and incredibly the lieutenant holds conversations with Detective Lucerne as an equal, as a colleague. Everything said by Detective Lucerne is good analysis and exactly reflects the mind of Lt. Columbo, so that he very eerily seems to be talking with himself, with his ideal persona, and when he tries on Detective Lucerne's snazzy hat and elevator shoes in the actor's dressing room, there's a certain shiver (or as film critics say, a frisson) in the back-and-forth of the imagery, and this is as much what is expressed as anything else.
The studio locale is utilized for comic interiors (the lieutenant stumbling through a hot set) and poetic exteriors: on the shore of the Universal lake, the director hurriedly lays out his shooting schedule as the mechanical shark raging in the background stimulates Lt. Columbo's curiosity.