Burke's Law (1963) : 1x10

Psychiatrist Eric Techman calls Burke to report that he fears one of his patients is a homicidal maniac who plans to kill him. Before he can identify the person in question, he is shot in the back. Burke convinces both Techman's secretary and his wife to not reveal the fact of the kind doctor's murder until Burke can question the five most likely patients: a stripper, a movie starlet, a Texas oil millionairess and her wild son, and a ski instructor (and sometime kleptomaniac).