Who is liable if a neighbors tree falls on my property causing damage to a vehicle?

As a general rule, if a neighbor's tree was healthy and blew down in a storm then they are not responsible for any dmage that was caused. It was an Act of God. If, however, the tree was dead/dying and fell, then they are responsible.

It all comes down to negligence. What did the neighbor do or not do that caused the damage? So, for example, was the tree visibly sick or ailing; was it too top heavy generally; were its roots damaged by anything the neighbor had done (such as by cutting into them to insall a patio, walkway, etc. nearby); was the tree leaning before it fell? If so, then the neighbor was negligent; they had a responsibility to take the tree down since it was a hazard that they knew or should have known of.

On the other hand, if the tree was healthy the neighbor did nothing wrong. It's not negligent to own a tree. You can't hold someone liable unless they were negligent and you can't impose liability if they had no way of knowing of the danger.

So you will have to prove negligence on the part of your neighbor's, in order to impose financial responsibility on them.

As for your car, your coverage may be an issue. You would have to have comprehensive (fire, theft, vandalism, falling objects, glass, etc.) in order for it to be covered. If you don't have this coverage, you'll have to pay for the damages out-of-pocket if you can establish liability on you neighbor's part.