I believe you can cut any of the limbs that cross over the property line without his permission. If the Tree is planted in such away that cutting the limbs will not be sufficient then I would take him to small claims court. The rules are less formal and he cannot have an attorney represent him.
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Not sure why you haven't removed the offending limbs at that point where they enter the airspace over your property. May want to 1) consult with a property law attorney in Alexandria and 2) let the neighbor know your plans so as to avoid a police issue, 3) consult with a certified, bonded, insured arborist before removing the limbs, 4) hire insured, bonded, licensed experts to remove the limbs, 5) in consultation with the local property attorney, determine if any part of the costs incurred are recoverable from the neighbor, 6) consider small claims court for any past damages.
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