A technician will typically check the filter, thermostat signal, igniter, flame sensor, pressure switch, and venting, then read any error code the control board is flashing. On older units they'll also look at the heat exchanger, since cracks there can let exhaust into the air you breathe.
Repairs to an existing furnace often need no permit, but a replacement does. In East Bridgewater, gas permits go through the Building Department, where the plumbing and gas inspector works, and the town's online permitting system handles the filing. Propane installations involve the Fire Department, and duct changes may need a sheet metal permit.
If the conversation turns to replacement, ask about the ducts too. Ductwork in a 1970s or 1980s house can leak or be undersized, and fixing it at the same time can make a new furnace or heat pump work far better.