Prescription: Murder (1968)

A psychiatrist who is married, is having an affair. His wife threatens to divorce him and take him to the cleaners if she ever catches him. So along with his mistress he plans to kill her and make it seem like she was killed by an intruder. He goes out of town as part of his plan and returns to find the police there investigating and the man investigating is Lt. Columbo. Columbo is a little odd and he asks the man some questions that he finds intrusive. Columbo continues to question him and the man's friend an ADA warns Columbo to watch his step. But Columbo goes on.