You have a right to cut off branches or roots that stray into your property, but you may not harm the tree. You are responsible for the cost of trimming. There are some limitations to this right of self-help. You may only trim to the boundary line, you may not enter your neighbor’s yard without permission (this is considered a trespass), and you may not remove the tree or injure it in any way. If you don’t follow these guidelines, you may be liable for damages and/or trespass. If the job is a big one, it might be wise to hire a professional to make sure it is done correctly and to avoid harm.
Because it can be costly to trim a tree, you may want to first try to resolve the problem with your neighbor. Perhaps the neighbor will split the cost with you, or will take care of it himself/herself to ensure the tree is not damaged. If the neighbor objects after you speak with him, it is a good idea to write a letter explaining the situation, your rights, and your intentions. You usually cannot sue because someone does not trim a tree. If it is a case of substantial damage or a serious impairment in using and enjoying your property, you may have some cause of action.
Ownership of a tree is determined by the location of its trunk. If the trunk grows entirely on your neighbor’s property, it is his tree no matter how far the branches protrude or the leaves fill your yard. If the trunk grows on the boundary of the properties you and your neighbor are both owners and are jointly responsible for the tree. You may not remove a boundary tree without permission from the co-owner.
For more information, see: Jordan, Cora, Neighbor Law: Fences, Trees, Boundaries & Noise, Chapters 3-6 (4th ed. 2002); Warda, Mark, Neighbor vs. Neighbor (2nd ed. 1999).