Since it’s your tree, it’s your insurance that pays for removal of the tree and any damage from the tree. However, debris removal coverage under homeowners insurance can be very specific and is only available if there is enough money left over after repairing the damage. Since the tree fell in your neighbor’s yard, most likely it didn’t damage any of your property. If the tree fell on their yard, you probably wouldn’t be covered for the removal, because wind damage to trees, shrubs and plants is normally excluded from homeowner’s insurance.