Title: The Dark Mirror
A woman suspected of murdering her doctor boyfriend has an identical twin sister. When both twins have an alibi for the night of the murder, a psychiatrist is called in to assist a detective in solving the case. Through a series of tests, he discovers which twin actually committed the crime and in the course of his investigation he falls in love with the normal twin.
Nunnally Johnson (written for the screen by), Vladimir Pozner (original story)