The answer to this question is not always straightforward. If there was noticeable, pre-existing damage to the tree that was neglected, the property owner (where the tree came from) would be responsible for removal costs and for any damages caused to your property. However, if the damage occurred because of an unforeseeable event, such as a violent storm, your insurance company will likely deal with the fall out. Additionally, if a healthy tree falls but no damage occurs, you more than likely will be responsible for removal costs on your own property.