Take pictures of the tree before you trim it. Make sure it's clearly established that the tree is encroaching on your property. You should also write a letter to your neighbor explaining your intended course of action if they don't address the problem.
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I agree with Mr. Copoulos but write separately to add that you should try to trim as close to the property line as possible. Common law provides that you own not only your land, but everything above it and below it. Trim only what's yours.