If the tree is on your property or that which you rent, most likely your auto (other than collision, or comp) coverage will be triggered. If it's the neighbor's tree, then theirs is going to have to pay. But to be sure, ask your agent and when you do, make a note of the date and time and name of the person you spoke to and keep that note with your insurance paperwork. You should always make such notes when speaking to insurance people.