Brijendra Pratap Singh (45), posted along with another Constable at Nautala branch of Allahabad Bank, died after he was hit by a bullet from his service rifle, they said.
Singh was initially taken to a district hospital from where he was referred to Trauma Centre in Lucknow, but he succumbed to his injuries on the way, police said.
Superintendent of Police Mohit Gupta said an enquiry is on to ascertain whether it was suicide or the rifle went off accidentally.