Trees can be tricky, but for the most part homeowners are responsible for what falls into their own yard. So if a storm causes your neighbor’s tree to fall in your yard, your homeowner's insurance could help cover the cost of removing the tree and remedying the damage it caused on your property, after your deductible.
The same is true in reverse: If a tree on your property falls in your neighbor’s yard, your neighbor should contact his or her insurance company to determine what type of coverage is available for damage or cleanup in their yard.
In most cases, neighbors are able to work things out without too much trouble. Depending on the extent of the damage, you may need to file a homeowners insurance claim. Your homeowners insurance may or may not cover the cost of tree cleanup, depending on your policy and the company you work with.