If a tree falls down from a storm or other natural cause and results in damage it should be paid by insurance. The problem is, whose insurance and who has to pay for the deductible? The property owner of the yard with the fallen tree should call their insurance agent.
Although, if it did not fall because of a natural cause, that is a different story. If there is proof that the tree owner knows the tree was dying, it is their fault and they are in charge of paying for it. The tricky part about that situation is that there must be proof that the owner knows and was asked to get it removed.
What if a tree doesn't fall from natural causes?
If your tree falls on your property:
You pay. In this case, you probably will not get help from your insurance if you did not maintain your tree’s health.
If your tree falls on your neighbor's property:
You will pay if there is proof that you knew or were warned of the unhealthy tree. Otherwise, there will probably be a dispute between insurance companies for fault.
If your neighbor's tree falls in your yard:
The neighbor (tree owner pays) if there is proof that they knew or were warned of the unhealthy tree. Otherwise, there will probably be a dispute between insurance companies for fault.
If a city-owned tree damages your property:
Call the local government and see what they suggest. They will probably send someone out to have it removed. They will also have to pay for your damages if they were warned that the tree was unhealthy.
If another person's tree falls on your car:
If you have comprehensive coverage, your car insurance should pay for the damage. If you do not have comprehensive coverage, the only way you will have a case to make your neighbor pay for the damage is if you can prove they were negligent.
If your tree falls on a car:
The car owner's insurance should cover the car damage if they have comprehensive coverage.
*Note that in any of these situations if no damage was caused by the tree falling, insurance will not pay for anything.
Overall, the best way to avoid this issue is to get dying or diseased trees removed as soon as possible. If it is in your yard, call a professional arborist to get it removed.
If you notice one in your neighbor's yard, contact them with a written notice that it should be removed and take pictures of the problem. Do not take action yourself or you could face a lawsuit for changing their property without permission.
After a tree falls, next there will be tree trimming and removal costs.