If a tree falls on your car, does your car insurance company have to pay?
Answer: Probably not.
Most people do not get insurance on their car against acts of nature/god/etc. The vast majority of people get liability insurance, and possibly theft insurance.
So if a tree falls on your car, your car insurance probably will not cover it unless acts of nature was covered in your insurance.
But if you have homeowners insurance which covers such accidents, and it is your tree on your property, then it is your homeowners insurance which will pay to repair or replace your car.