High winds and storms can cause trees and large branches to fall, sometimes landing on the neighbor’s property (including their car). If in fact the tree is healthy otherwise, you are most likely not negligent.
So your own policy would not pay the neighbor for their damage and they would have to file their own claim. But let’s say for example you are aware that the tree has issues and do nothing about it, you would most likely be found negligent and it would be your claim.
You’re typically only considered responsible if neglect on your part was a contributing factor to the tree’s demise.