I believe the song title you are seeking is entitled, 'Street Scene', written by Alfred Newman, from the 1931 movie of the same name.
The aforementioned film has experienced a Renaissance precisely because everyone wants to know where the Mike Hammer theme originated.
It is certainly very haunting, and I personally spent many years seeking out the sheet music, which was very difficult to find in the 1960s.
It is a great composition, and I admire anyone's taste in music who has spent any effort to seek out this original classic.
Houdini