Sheesh! Why is that guy (Smitty's neighbor) freaking out over some
branches? Some people...

I've got exactly the opposite situation: the offending trees are on my
property, and the branches overhang my neighbor's lawn. She's an elderly
widow. When the branches cause trouble, she tells me and I trim them. No
big deal.

Trees have strange rules, as others have pointed out. Here's a
couple of examples from NJ:

A neighbors tree fell during a storm, crossing the property line. No
damage was done. After contacting insurance companies, the parties
learned that they were each responsible for the part of the tree that was
lying on their respective properties. However, since no damage was
done, no insurance claim would be paid.

During another storm, my one of my neighbors trees fell across my property
line and smooshed my fence. My insurance company paid to clean up the
part of the tree on my side of line (they left me all of the stuff good
for firewood), and repaired my fence. My neighbors insurance company
didn't pay anything, because there was no damage on his side. I did help
him cut tree into firewood.

--
Ron DeBlock N2JSO
If God had meant for Man to see the sunrise,
He would have scheduled it later in the day.