Columbo - "Prescription: Murder"

Dr. Ray Flemming, a psychiatrist, kills his wife and convinces his mistress, an actress and his patient, to help cover up the crime by pretending to be his wife on the couple's plane flight. Certain of the doctor's guilt, seemingly befuddled Los Angeles Police Dept. Lieutenant Columbo painstakingly searches for the fatal flaw in this so-called perfect murder.