Under the law the Park owner would be required to maintain the trees on the tenants' lot UNLESS it is expressly provided to the contrary that this will be the tenant's duty under the prospectus and/or the lease to maintain the trees on the lot they are renting.
Unless your tenancy agreement states otherwise, you can safely assume that you (the tenant) are responsible for mowing and edging the lawns, watering, weeding, pruning and fertilising ? all chores which could be deemed 'garden maintenance. '
Short answer: It's legally and financially the landlord's responsibility unless otherwise stated in the lease.
If branches from a neighbor's tree are hanging over onto your side of the property line, you have the right to remove those portions of the tree that encroach on your land. It doesn't matter whether or not the overhanging branches have caused damage to your property.
(1) Comply with the requirements of applicable building, housing, and health codes. (2) Maintain buildings and improvements in common areas in a good state of repair and maintenance and maintain the common areas in a good state of appearance, safety, and cleanliness.