The deceased, identified as head constable Chandpal, shot himself around 8.15 AM, said a senior police officer.
His duty hours were from 7am to 1pm. He had been posted at the Supreme Court since April 2014.
The cause of the suicide was not known yet, the officer said, adding crime and forensic teams were on the spot.
Police will be questioning Chandpal's family members and colleagues to ascertain the reasons for him taking the extreme step.