Liability for tree, how to transfer back to neighbor?

[Jack B.]

My neighbor at a house I recently sold wanted me to cut down a tree that he felt was a danger to his property, conveniently he did this right after I called the cops on him for repeatedly parking in my driveway and refusing to move his vehicles...

The previous owner mentioned to me that she had wanted to take the tree down but this same neighbor didn't want it taken down since his kids played around it. This adds fuel to my theory that he merely did this for retaliation. I told the neighbor that the tree looks the same as it did when the house was built a few years ago, what makes him think that it's a danger? He responded by getting a guy from 120 miles away who had been an arhborist for 6 months at the time (mind you we live in a major city, there are dozens of arbhorists within a few miles of us...he was shopping for someone who was purely new and would say anything for business IMO) to illegally trespass on my property to assess the tree. He then sent me a certified letter with the results and requesting the tree to be taken down (which I had previously told him he could do at his own expense via text when he had originally contacted me).
Fast forward, a year later I sold the house. There was nothing on the seller disclosure form (form 17 for WA) to put a note about a tree. I'm not sure if the neighbor has contacted the new owner about the tree, but I want to make absolutely sure that the neighbor doesn't have a claim against me if the tree falls on his property.
Should I send him a certified letter and if so, what should I tell him? To contact the new owner of the property about the tree?