Who is responsible for vehicle damage if a tree falls on it during a storm?

It's called an act of nature. No one is liable for acts of nature. Simply submit a claim to your auto insurance. You'll be responsible for the deductible but they'll cover the rest.

There's a chance someone could be found At Fault if the tree was rotten, not rooted correctly, grossly overgrown or otherwise unstable enough to fall, but you'd have to prove that 1) the people responsible were aware of the problem and 2) they refused to fix the problem.