The police can check to see if the car is reported as stolen.
If not, unless it is on the street, they can not do anything. If you notice it being driven without plates, then you can report it and they may be able to at least fine the owner.
The apartment management is the only ones (as previously stated) that can request the towing.
If the note does not accomplish anything and the apartment management will not enforce the parking allocations, rather than damaging the car, try to jack up the drive wheels and slip a cinder block under the axle. The block will not show and yet the car will not be able to be moved.
However, you may start a war with the neighbor no matter what is done if you escalate the situation.
If the apartment complex will not enforce the parking, determine the square footage of the parking area and withhold that percentage from the rent. Just make sure that you document the complete situation using dates with a cover letter on your rent payment.