Fault would depend on why the branch fell. If the branch became detached from the tree due to a storm, it would be covered under the homeowners policy.
If it fell because you struck the tree with your vehicle and the branch fell off as a result or another likewise scenario, you might be considered liable for the damages to your vehicle through your auto insurance. This would be considered an collision
claim, depending on the details. I would recommend contacting your insurance company first to let them about the incident.