A 37-year-old man was shot dead inside a Brooklyn public housing development, police said Tuesday.

The victim was found dead shot in the head in a first-floor stairwell near the lobby of a Nostrand Houses building on Batchelder St. near Avenue V in Sheepshead Bay about 11 p.m. Monday, cops said.

His name was not immediately released but cops say he lived in another part of Brooklyn.

No arrests have been made and a motive has not been established.