Don't even respond to accusations or questions, except to politely inform them that you have no idea what they are talking about. Put nothing in writing that acknowledges anything other than receipt of their accusations or questions.
If questioned by any authorities, deny any recollections of the event, but never tell a provable lie. Decline to answer more until they serve you a subpoena for your records. Yes. This is a blatant stalling technique. It might also prevent a scum-sucking bottom feeder lawyer from thinking there are deep pockets he can stick his greedy fingers into.
Once contacted by ANY authorities (lawyers or police), notify your insurance company, pronto. NOT before then, either. The insurance companies like to use that sort of thing to raise your rates, and they like to quickly settle claims without actually establishing any liability. Once an insurance company is aware of a claim, they contact everybody involved, and now the neighbor has located some deep pockets to send his lawyer after. If the aggrieved neighbor asks you who your insurance company is, tell him that you are just an uninsured hack, and you can't afford that crap.
To the neighbor, (in person only) defer any questions about whether you were ever there or touched the tree, unless they have photo's or other proof. Answer questions with questions! THEN they will have to get the neighbor involved, testifying that she hired YOU, not someone else. At that point, she has admitted that she hired you to do the offensive action, and she will be obliged to admit some or most of the responsibility.
This kind of action, while less than honorable in my opinion, are the sort of things that should be done when you have your buttocks hanging in the breeze, exposed to a vicious lawyer.
Good luck!