The cities in my area, no police would tow abandoned cars on private property. As suggested earlier, the health department could have it towed it if it presents a health danger. In another city the property owner has to post a no parking sign in plane view citing codes and contact phone number and if the car has an expired registration the property owner has to paid the tow.
I once had a car abandoned in front of the driveway for a week (public property) and I had to show the police its was an active driveway with a working garage before they would tow it.