Towing Issues: Towing from private property laws in CT, plain nuts, apartment managers

Question
Hello, I live in CT. in an apartment complex. There is no assigned parking and capacity is about 50 % full. There is a posted sign on the property that states unregistered vehicles will be towed.
My daughter recently inherited her grandfathers car, however she doesn't even have her license yet, so she made arrangements with my son , who does not live here, to use it until she can take it over. Her deal with him is he can use it for work only and must return it at night.
Now, my manager is saying that the car can not be here. He says that all cars must be registered to lease holders only ~ that would be me. He said cars registered to other people can not be on the property. This sounds plain nuts to me.
A simple solution would be for me to register it, but I don't want to be liable if he has a problem with the car.
There is nothing in the lease stating cars must be registered to lease holders and I was told when I moved in that I was allowed to have 2 cars. The other issue is I know of at least 3 other tenants whose cars are registered to other people. Seems they are making up rules just for me.
Can they legally tow it, as they're claiming they will ?

Answer
Well apartment managers have all sorts of power and privileges  and as such enforce rules as they see them...

As to vehicles being registered to other people I wonder what would happen if you have a rental vehicle while yours is being worked on... Its not registered to you !

That being said, other people having vehicles not registered to them and enforcement of the rules, reminds me of a statement a state trooper told me one day...

I asked him how he responded to the comments about why did you stop me when I was traveling in a pack of vehicles all exceeding the speed limit...
His response was, "ever been fishing ???  Ever catch ALL THE FISH"

It would seem that they could tow the vehicle, but a court of law might determine that is was not legal to tow it. Every time something is towed, there are so many small things that can go wrong to invalidate the tow reasons...
I would talk to the manager more and see what "HAS TO BE DONE" to solve the problem, leave all the other violators out of the discussion as that can just make him madder at you and look for reasons to bother you..