...you could draft a simple release , both parties sign and dated. A legal document for the cost of a Bic pen. Ten minutes.
In my next of the woods if a tree falls over the property line of the neighbor your job ends at the property line. I get both parties to sign off on my standard work order, one order per property.
... it is one thing to build a pool under a tree but then force, the neighbours into pruning it because of leaf material dropping into it is crazy ...