comune

A comune is a unit of local government made up of a main town and the territory around it, run by a mayor (sindaco), a board and a council. The word also means the town hall offices, as in sposarsi in comune, to marry at the town hall.

Civil registration was organized by comune, so you need the right one to find an act. A comune can include outlying hamlets called frazioni whose names may be what your family remembered. As an adjective comune also means common, as in nome comune.