In a commercial building, namely a fire house, with sleeping quarters, do the circuits in those rooms need to be arc fault protected.

Good question.

This will be determined by the use of the space that is used as a dwelling unit.

Only that space would be required to have AFCI protection, not the "commercial" portion of the building.

This certainly will be subject to the decision of the AHJ.

Sure sounds like a good idea, but separating the space and wiring may prove to be challenging depending on the actual arrangement.