Zonal Inspector General (IG) Kundan Krishnan said a woman and a 12-year-old boy were killed in the incident which took place at the Madanpur block headquarters.
The identities of the deceased persons is yet to be ascertained.
Police said five persons were injured in the melee which ensued as a rsult of the firing.
Aurangabad Sub-Divisonal Officer (SDO) Bhim Prasad said that police personnel at the Madanpur block HQ fired in self- defence after a mob attacked them and tried to ransack the office buildings.
Officials said that people in villages around Madanpur were agitated over search operations conducted yesterday night by police and CRPF jawans during which the personnel allegedly misbehaved with women and elderly persons.
The villagers were today holding a protest at the Madanpur block headquarters demanding action against the guilty police and CRPF personnel.