Damage to your own or neighbors home resulting from a fallen tree most likely will be covered by homeowners (HO) policy. If this is your tree that has damaged your neighbors house or property, your should have personal liability coverage within your HO policy.
Claims coming from fallen trees that as a result of fire, wind, lighting, hail are usually covered by an HO policy.
The landscaping itself may be covered under Coverage C on your HO policy or under Tenants Betterments and Improvements coverage on your Business Personal Property coverage.
There are certain exclusion to each insurance policy. Bad soil, over watering or insects are usually excluded from coverage.
You can talk to your agent or call your company’s claims department and ask them specific questions about the fallen trees coverage.