General liability policies, both personal and commercial, exclude coverage for auto liability. Auto liability is its own risk category and is typically insured in its own policy. If you hit somebody or something with your car, look to your auto policy for coverage.
What if you hit somebody in you car?
The standard general liability exclusions preclude coverage for liability arising out of the ownership, maintenance, use, or entrustment of an auto. Does an injury arise out of the “use” of a vehicle when the vehicle is merely the place that the injury takes place?
See Indiana Ins. Co. v. Auto-Owners Ins. Co., 260 Mich. App. 662 (2004).