The incident took place yesterday afternoon when Ram Kumar was alone at his rented accommodation in Bindapur which he shared with a person, they said.
He was posted with the Dwarka North police station in South West district.
"Kumar latched the door from inside and shot himself using his service revolver. The incident came to light when his roommate returned home in the evening," said a police official.
A police team which reached the spot took Kumar to the nearby Deen Dayal Upadhyay (DDU) Hospital where he was declared 'brought dead'. His body was sent for postmortem.
Investigators are questioning Kumar's roommate and his neighbours.
Kumar's family which lives in Rajasthan has been informed. He is survived by his wife and two children.