Trees that fall across property lines cast shade into your yard, drop leaves and add to yard management. If you're unhappy with the size of a neighbor's tree, it's your job to trim overhanging branches, within reason.
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Even though the tree is on your neighbor's property line, trimming branches that fall over on your side, such as those coming over a fence, is your responsibility, according to the American Bar Association. You can trim the part of the tree on your side at any time.
Legally, you can't remove the tree altogether or cit it back enough to kill it. You also can't trespass onto your neighbor's yard when pruning, unless the tree is about to cause serious damage to your yard.
When you're planning on trimming back a neighbor's tree, the American Bar Association recommends talking with the neighbor to give him a friendly heads up. Even if he objects to your trimming the branches, you still have the right to trim.