The official, speaking on condition of anonymity, said the fighting broke out yesterday in the town of Bimbo south of the capital after members of the Seleka rebel coalition "stole and hid" several vehicles.
He said military police had gone to recover the vehicles, but the alleged thieves resisted and one of the rebels was shot by the officers.
In retaliation, one of the rebels "opened fire on a member of the military police", who also died.
The police official said the multinational peacekeeping force FOMAC intervened with the back-up of French troops and restored calm to the town.
The Seleka rebel coalition seized power in Central Africa in a coup ousting president Francois Bozize after a peace deal fell apart.
The security situation in the already unstable nation remains volatile with pillaging and sporadic attacks still not brought under control.