Sanjay Kumar Tiwary (40) was shot dead at Shamkauria under Isuapur police station while he was on duty, Zonal Inspector General (IG) Paras Nath said.
Chief Minister Jitan Ram Manjhi expressed grief over the incident.
"Tiwary had gone in his jeep to help employees of a petrol pump in the area in depositing cash in a bank branch. It was when he was returning that a few unidentified persons stopped his vehicle and fired at him," the IG said.
Tiwari died while being taken to hospital. His body has been sent to Chapra Sadar Hospital for post mortem examination.
Senior police officials including SP Satyaveer Singh and others have rushed to the spot.
Narrating a different sequence of events, Chief Minister Manjhi told reporters, "According to my information, the SHO got a tip-off about a dacoit gang assembling. As he and one more person were proceeding to the bank, they were shot at by few people.