What is my recourse if branches from neighbor's tree pose a potential hazard?

Question Details: Our neighbor has a tall tree with many large branches that extend over our property. Many of the branches are dead. I'm concerned that if some of the branches were to break and fall, they could cause injury or property damage. I've asked my neighbors for permission to have a professional tree trimmer climb their tree to remove only those branches that extend into our property but the neighbors have refused unless I agree to pay to have their entire tree removed they don't want the tree on their property either but don't want to pay to deal with it. If a limb were to fall on our property and cause harm or damage, I assume they would be liable, but am looking to understand the law on this case. Also, what I can do preemptively to deal with the branches so that we don't have to worry about someone getting hurt or property damaged? There's unfortunately no other way to remove the branches than to have someone climb the tree. The tree is beyond reach of a truck or crane.

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