The discovery was made around 7:45 a.m. Monday at the Linden Knoll Condominiums, located on the 3600 block of Hewn Lane in Pike Creek.
The body of a man, who is believed to be in his 60s, was found on the overhang of the entrance door.
The identity of the victim is unknown at this time.
It is not known how the man got on the overhang. Police say there were no open windows in the building.
Police are calling the man's death suspicious.