Act of God
In most cases, a tree falling is considered an “Act of God.” An Act of God is the legal term for when an event is outside human control. A healthy tree that was blown over due to high winds could not be foreseen or prevented by your neighbor, so he is not responsible. In these cases, you are responsible for any damage caused by the tree, including removing it.
Reasonable Care Standard
Your neighbor may be responsible for the tree if she failed to maintain it. The owner of the tree must meet a “reasonable care standard.” In layman's terms, this means that your neighbor was negligent and could have prevented the damage. If she failed to remove damaged limbs or if the tree was unsound and not removed, then she may be liable for damages that the tree caused. Since the action could have been prevented, it is not considered an Act of God. However, you must be able to prove that the owner was negligent, which is not always easy to do.
In many cases, your homeowner's insurance policy will pay to remove trees that have damaged your property. If your neighbor’s tree damages your property, then you need to report it to your insurance company. The insurance company should pay to remove the portion of the tree that is on your property and repair any damage it caused. Insurance companies may not pay to remove trees that fell but did not do any damage.
Repairing the damage done by the tree can be much easier then repairing the damage done if you argue with your neighbor about the damage. If your insurance company will not cover the cost of removing the tree, talk to your neighbor. He might be willing to split the costs of having the tree removed or help you remove it. Even if he is liable for the damages, he certainly didn’t intend for his tree to fall and is probably upset as you are about what happened.