Welcome to the club—neighbors who have a dispute about trees. To avoid an unpleasant dispute (or your neighbor trimming your tree on their own—and possibly botching the job), talk with your neighbors and find out exactly how much tree trimming would do the trick. If it’s not too much, and doesn’t affect the health or aesthetics of your tree, consider making the trim. Your neighbors may be willing spring for the cost of the tree trimming (or at least split it). But you should hire a professional tree service to do the work , to assure a quality job that keeps your tree healthy and aesthetically pleasing.
If you are firmly opposed to trimming your tree—perhaps it screens your view of your neighbors’ unsightly back yard—check your local tree ordinance to make sure the law is on your side. You may be violating local law if your tree (no matter how beautiful) presents a hazard to your neighbor (for example, if dangerous limbs hang over the neighbor’s property), violates any height limits or view ordinances, or straddles the property line. If you’re breaking the law by refusing to trim your tree, the results may be more than a bad relationship with your neighbor; you may find yourself in court if your neighbors sue you for interfering with the use and enjoyment of their property,
You can find out local tree rules by calling your building or planning commission or checking local ordinances online. If you can’t find yours, check out State and Local Government, and if your house is part of a homeowners’ association with CC&Rs, make sure you check these rules, such as restrictions on tree heights.
See the Nolo articles on Neighbors and Trees for advice on handling tree disputes with neighbors. The Nolo book Neighbor Law, by Cora Jordan and Emily Doskow, provides extensive advice on tree-related law and liability issues involving invading branches, damage from an unsound tree, boundary trees, and more, including how mediation or small claims court can help resolve tree disputes.