The officers, from Bisrakh police station, allegedly got drunk while celebrating Holi and went on a ride in the SUV, a white Tata Safari.
Witnesses said they saw the SUV leave the police station at high speed and hit two women and two children passing by. The vehicle went out of control and rammed into a wall, killing one woman.
One of the police officers has been identified as Rajiv and a case registered. "We are investigating if he was drunk," said a police officer.
It is not known who the SUV belongs to. The injured have been admitted in hospital.