The Hollow Man - John Dickson Carr

A man has been shot in his locked up study. The only way for the perpetrator to escape is out of the window and through the backyard or over the roof, but in both cases there are no footprints on the blanket of snow around the house.

 

Definitely a locked room mystery. I have never heard of John Dickson Carr before, but supposedly he is one of the masters of this genre.