The Naked Face by Sidney Sheldon

Dr. Judd Stevens is a psychoanalyst faced with the most critical case of his life. He needs to penetrate the mind of a murderer. If he does not, he will find himself arrested for murder. Or be murdered himself.

Two people close to Dr. Stevens have already been killed. Is one of his patients responsible? Someone overwhelmed by problems? A neurotic driven by compulsion? A madman? Before the murderer strikes again, Stevens must strip away the mask of innocence the criminal wears, uncover his or her inner emotions, fears, and desires, and expose the naked face beneath. But who could it be?