Trees that grow along property lines can become a point of contention between neighbours. This is especially true if the tree is a nuisance to one person but not the other. A tree that drops messy fruit into a neighbour's pool, for example, may be a huge nuisance. You may think the location of the trunk of the tree determines who can trim or prune the tree, but this is not always the case.
If your tree has branches and limbs that protrude or hang down onto your neighbour's property, he can trim them back. The same is true for roots that creep onto your neighbour's property. Common law sides with your neighbour in every state. Pruning should be done carefully, however. If your neighbour is excessive in his pruning and harms or kills the tree, he can be legally held liable for the replacement cost of the tree.
Interestingly, although your neighbour can prune the branches and roots that are on his property, he can't step foot onto your property to do any trimming. If he climbs on a ladder and leans over the fence to trim the branches on your side, he is breaking the law. And, while your neighbour is free to trim the branches to the property line, if those branches hold fruit, he can't have a snack without your permission: That fruit is considered your property, not his.
If fruit falls from the branches of your tree into your neighbour's yard, he may or may not be free to eat it. There is no set precedent for this, and courts have ruled both in favour of the neighbour and in favour of the owner of the tree. Leaves are a different story, however. That fallen foliage floating in your neighbour's pool is considered a product of nature, and it is solely the responsibility of the neighbour to clean it up.
In some states and in some cases, it is your responsibility, not your neighbour's, to keep that tree trimmed. Several state courts have ruled that if encroaching roots or branches are causing serious harm to your neighbour's property, he may have the right to sue you to get you to control your tree. The same holds true for noxious trees. In Arizona, for example, a homeowner may sue her neighbour if a noxious tree is invading her property. As of 2008, California is the only state that allows homeowners to sue neighbours to force them to trim a tree that is not noxious or threatening to property.