I manage a 3-family rental in MA. I will try to keep my long story as short as possible. I promise it is relevant.

The house I maintain is 3 stories, with each floor being its own 2-bedroom apt. Up until last year, the whole thing was heated by one ancient boiler. It supplied heat to radiators throughout the house. There was one thermostat that had to be programmed so that everyone was at the required temps.

Last November the boiler failed and a new system had to go in as quickly as possible, but while still meeting the legal requirements of MA. The boiler failed in such a way that CO was released, so every agency that could possibly get involved was involved. The fire dept., the gas co., the health dept., the city plumbing inspector, and the plumbing co. that did the work.

The solution that we came to was to install what are called direct-vent furnaces in each apt. They are about 4' wide by 2' tall and 18" deep. The ones I have are rated at 38K BTU and are sized to sufficiently supply warm air to the 5-room apartments.

However, they are, as is OP's system, just one unit in each apartment. They are in the living rooms, as those are roughly the center of the apartments. There are no additional units, vents, radiators etc. in each room. The ideal scenario is you would leave the individual room doors open during the day and let them warm up.

The tenants and the health dept. initially balked a bit at this, but after a lot of research and back and forth, it was determined that this system satisfied MA laws.

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And so that's the point of this long post. It was my very recent experience that a properly sized and properly working central heating unit DOES meet the requirements of the Mass. health codes. This was not me interpreting the law, this was at least 3 professional agents of the local health department making a determination. They did not require that each room had its own heating source, as long as the proper temperature could be reached in each room.

(of course, this assumes the system is functional and appropriate, which may or may not be the case for OP)

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Thank you