Officers were called to Urquhart Drive in East Kilbride, South Lanarkshire, just after 2pm on Sunday.
They discovered the body of a man at the three-storey flats, believed to in his 40s.
The area was immediately sealed off and forensic officers were at the scene.
Officers were carrying out door to door inquiries and studying CCTV footage of the area in a bid to piece together the man's last moments.
A police spokeswoman said the death is being treated as unexplained. A post mortem was being carried out today.
A spokeswoman for Police Scotland said: "At 2.10pm yesterday police were called to a report of a man's body being found in Urquhart Drive in East Kilbride.
"A post mortem examination will be carried out in due course to establish the cause of death. However it is being treated as unexplained."
Meanwhile, another post mortem was being carried out today after the body of a man was found in a river in Kilmarnock.
The body was pulled from the Kilmarnock Water on Saturday morning, near to London Road and taken to Crosshouse Hospital.
The dead man was named locally as James Duffy, who was understood to have been from the nearby village of Crookedholm.
It is understood next of kin were being informed by police.
Officers sealed off the area and set up diversions after the discovery of the body.
A spokesman for Police Scotland said: "At around 11.50am on Saturday February 8, the body of a man was found in the water near to London Road in Kilmarnock."