Surfside 6

Surfside 6 is a 1960 - 1962 American detective series that aired on the ABC television network. It starred Troy Donahue and Van Williams as private detectives who run their office from a houseboat in Miami Beach. The show was one of several series developed by Warner Brothers for ABC after the success of the similar-themed 77 Sunset Strip.

Power of Suggestion (Season 1, Episode 8)
Miriam (Shirley Knight) comes to the agency with an unusual case- she believes that her employer, a magician and hypnotist who runs a mind-reading act, has hypnotized her to kill someone.