Check your taxing authorities. Central air/heat pumps are often considered additions/fixtures to the property and trigger a property reassessment. A window unit is removable transportable personal property and therefore not part of the physical property any more than is your refrigerator. Wyhen I moved into this house in 1981, it had a Carrier Weathermaker - Willis Carrier’s original system. It died (wiring lit up) in the late 1970s so I replaced it with a whole house fan and a $300 window A/C. 40+ years later still going fine. Amusing sidenote, the county was reassessing properties just at that time and when the assessor called to alert me to his visit, I told him the A/C now lived in the back yard and he removed it from my property description. Couldn’t miss it - about the size of a commercial double door refrigerator.