Question: What do I do if a  neighbor's tree is hanging over in my yard and it is damaging my car.

The owner of the tree is NOT required to trim his tree off of the neighbor’s yard. You cannot prevent them from trimming it. You are allowed to trim or cut the neighbors tree up to your property line, provided it does not cause irreparable long term harm to the tree. They are NOT allowed to come on your property to conduct the work unless they have an easement. The power company has an easement and can enter your property to trim trees, but the easement is their property, sort of. The power company will usually inform you that they are entering your property, but they are not asking your permission. In addition, you must use know safe trimming practices to prevent further damage to the tree. For example, if your cutting killed the tree you might have a liability issue. Unsightliness is not the issue, only death of the tree. If your tree is hanging on some one else’s property, you are not required to trim it off their property. That was just the way the tree grew. You cannot prevent them from trimming it off of their property.