The answer is "NO"! This issue is among the most misunderstood by the average person. Although you may feel bad for your neighbor and even feel somehow responsible, under “Tort” or “Common” law, the finding of legal liability requires that you be found “negligent”. A windstorm is considered an “Act of God”, a legal term for natural events outside of human control for which no one can be held responsible. This well established common law is why a claim of this type is almost always denied for liability.
This issue becomes clearer when you take your example from windstorm to tornado. Now your tree travels across town before falling on a car. You can see, for very practical reasons, no one is held legally responsible for natural disasters. You can’t have every neighbor suing each other for the variety of property flying everywhere. So, everyone must assume the risk of loss to their own valuables caused by events of nature.
If your neighbor didn’t buy “other than collision" (comprehensive) coverage for his damaged vehicle then he self-insured his loss. That’s not your problem. Your neighbor was gambling the value of his vehicle every day from any and all causes.
NOTE: Your neighbor may not want to get a legal liability lesson from you. Call your agent and have them explain this to your neighbor, keeping you out of the middle, and on good terms. In the unlikely event you are sued, your Homeowners policy contains protection for “Personal Liability” under Coverage E and will defend you up to your selected limit from claims of property damage liability, even if frivolous or groundless.
For answers to related questions click: Wind Damage ~ Am I Covered?