Brooklyn cops responding to a report of a man sleeping on a roof found the guy covered in a blanket — with a bullet in his head, police said Tuesday.

Timmie Glover’s body was found on the roof of a building at the Louis Armstrong Houses on Lexington Avenue in Bed-Stuy around 1:40 p.m. Monday, police said.

Workers from the New York City Housing Authority had called 911 to report a man sleeping on the roof, cops said. When police arrived, they discovered that the 42-year-old Long Island man — who was wearing several layers of clothing and a winter hat and covered in a blanket — was shot in the back of the head, police said.

He was pronounced dead at the scene.

Glover has a permanent address in Freeport but was known to frequent an apartment within the building where he was found, cops said. Police were looking into whether he had recently become homeless.