I just had something like this happen to me. During a recent wind storm, a branch from a tree in front of my house fell on a car across the street, causing over $2,000 in damage. The owner of the car contacted me immediately. I'm a new homeowner so I freaked out and called my insurance agent. She informed me, calmly, that unless someone can prove (or I admit to) negligence on my part, my homeowner's policy doesn't cover damage to OTHER PEOPLE'S PROPERTY. Apparently, in NY State anyway, that's the way it works. So if your car is damaged by someone else's tree, you have to file a claim with your own car insurance company. If the tree branch had damaged their house or garage, they would file a claim with THEIR homeowner's insurance, not mine.
That's how it works in NY State, anyway. . .
Lesley