In Minnesota, the owner of a motor vehicle is personally responsible for the negligent driving of any person operating the vehicle with the owner’s permission. So if you let somebody drive your car in Minnesota, and the driver causes an accident, you may be liable for the injuries and damages associated with the accident.
One purpose of this law is to encourage Minnesota vehicle owners to maintain sufficient liability insurance to make sure any losses and damages are covered, and the vehicle owner is not exposed to personal liability.
The applicable law is outlined in the Safety Responsibility Act, Minn. Stat. § 169.09 subd. 5a:
Subd. 5a. Driver deemed agent of the owner. Whenever any motor vehicle shall be operated within this state, by any person other than the owner, with the consent of the owner, express or implied, the operator thereof shall in case of an accident, be deemed the agent of the owner of such motor vehicle in the operation thereof.