Not exactly a mystery who did it. Spoiler
I'm 45 minutes into the movie and already figured it out. As for the elevator scene, I found it ridiculous how Angie Dickenson acted, slowly moving back and saying No, No. And the killer waits, then pounces? Why didn't she at least try to push her way out of the elevator? This movie may have been a thriller in 1980, but not today.
I imagine we were supposed to think the killer was the guy she slept with or her husband, or maybe just a psycho. Those would be too easy so naturally it would follow that the psychiatrist was the crazy killer.