In property-line tree matters, my understanding of the law (locally,
YMWV):
notification of owner that overhanging tree is a hazard makes owner
liable for damage triggered by "act of God",
parts of tree crossing property line may be cut at that line at
discretion/expense of cutter.

Cutting at the line presumes a few things, and can leave ugly stumps.
And ... stump likely will spring back some from the line to the delight
of lawyers. :')

Depending, you might negotiate allowing cutting party to cut back to
marked points that won't deface or damage tree. Watch out on allowing
neighbor to cut over the line on your side- a few years back, neighbor
had workers prune our tree about 8' back from line. Way more than
agreed to.

HTH,
J