Carolyn Wells 
Luminous Face 

The death of Robert Gleason, a wealthy businessman from Seattle, at first looked like a suicide. He had called his doctor saying that he was shot, and when the doctor arrived at his New York apartment, the door was locked. After breaking down the door, his body was found lying on the floor, a revolver at his side. Yet certain facts argued against a verdict of suicide. Gleason had been shot twice, once shot to the temple, which killed him instantly, and a second shot, after he was dead, to the shoulder. How could he have made a phone call after he was already dead? A web of conflicting clues and dubious alibis baffle the police until detective Pennington Wise and his mysterious assistant Zizi are called in to solve the case. (goodreads)