May be going out on a limb here....
In my neck of the woods, if the limb is over the property line then a home owner has the right/responsibilty to trim that portion of the tree. So if a dead limb overhanging your property breaks off, then you own the consequences.
If the tree falls over that is another matter, however I would go to my insurance company for coverage. It would be up to them to deal with the neighbor's insurance company.
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