Yes, homeowner insurance policies typically cover damage caused by fallen trees. However, the coverage may vary depending on the specific policy and the circumstances of the incident. In general, homeowner insurance policies provide coverage for damage caused by falling objects, including trees. This coverage usually includes the removal of the fallen tree and any necessary repairs to the property. It's important to note that coverage may be subject to certain limitations and exclusions, so it's always a good idea to review your policy or consult with your insurance provider to understand the specific details of your coverage.