Fyi, you are allowed to trim what is hanging into your yard, even though the tree is theirs. Just as a courtesy, you should speak to your neighbor about it first, and follow up via written letter sent certified return reciept. If they are objecting to your request, you still can do it yourself but don't access the tree from their side of the property, take photos of the area and tree in question before, during and after doing the work. Be cautious not to have any tree limbs or saws fall onto their side of the property and you are responsible for the proper disposal of any and all tree limbs or debris.