This is debated in many regions every year. It is going to vary state to state. You will need to know the law. Don't believe what the city tells you just because somebody on the other end says so. I'm my area, no matter where it is rooted, whatever falls on your land is your responsibility. This law only applies in an act of God. If the neighbor or city fells a tree, they are responsible for the cleanup. The only exclusion to this law is where you the homeowner sends a registered letter to the owner where the tree is rooted prior to the act of God i.e. ( you have a tree that we as homeowners feel is in danger of falling and damaging my property). At this point the owner where the tree is rooted is responsible. As you can see, this can be debated. I would know my law before I did anything.