Expect a site visit with measurements, a heat loss calculation, a look at ducts or room layout, and a check of your electrical service. A good proposal names the outdoor and indoor units, their locations, the line set routes, and whether your existing system stays as backup.
Kingston's SmartGov portal accepts electrical, mechanical, and gas permit applications, and the wiring inspector at Building, Inspections & Zoning handles the electrical side. If the job also removes an oil burner or tank, the Fire Department permits that part and schedules its own inspection. Larger projects that need a building permit follow the department's filing checklist, which includes Stretch Code information and 110 mph wind design details.
Installation itself usually takes a few days for a whole-home system, longer if electrical upgrades or tank removal are part of it. Ask how the house will stay heated in the gap between the old system coming out and the new one passing inspection.