Can My Private Parking Garage, Who Assigns Spots For All Vehicles, Require Me To Park In A Handicapped Spot (i Am Not Handicapped)?

I live in New Jersey. My apartment building has a parking garage underneath it, which is private and managed/owned separately from the apartment building. The parking garage assigns all vehicles to a specific spot. They moved me from my first assigned spot, as they accidentally double rented it. The new spot they told me to use is marked as a handicapped spot. I told them that I am not handicapped, and they told me that it wasn't being rented right now so they will assign me there, and if anyone in the future needs a handicapped spot, they will move me and reassign my spot.
I can't just park in another spot because they are assigned and I'm not even sure which are open or which ones could get me towed for being in someone else's spot.
The parking garage is private, and you need a card/code to enter, so it's not a spot like you would find at a public, commercial place (like a shopping plaza or something which I would absolutely never park in).
I'm asking them if they can revise the spot to remove the sign if they truly don't need it (there are other handicapped spots, and I know some of them are assigned, and overall the garage is pretty full so I don't know that they have many other places to move me). Of course if someone ever does I am definitely willing to move, it's just that the parking garage insisted that I have this particular spot.
Other people who park in handicapped spots don't hang their cards, I am assuming because it's a private garage with assigned spots so there's not really a need - there's no police enforcement doing ticketing or towing in the garage.
I'm just nervous that someone would call to have my car towed, plus it's just not a good look parking in a handicapped spot when you don't need it. The garage does know my car is assigned there so if they had a complaint to tow, I assume they would say that the car is in the right spot.
The building is not new (built in the 1920s and converted to modern apartments maybe 20 years ago), so I'm not sure what accessibility laws apply for how many handicapped spots they need etc.
My question... Can I get towed from my assigned spot in a private parking garage?
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