The Minnesota No-Fault Act (MS.65B.48), requires owners of registered motor vehicles to maintain no-fault insurance. The law makes it a crime for a vehicle owner to operate or permit operation of any uninsured vehicle upon any public road, street or highway.
Wording of this MN Statute goes on to say that every owner of a motor vehicle which is required to be registered or licensed or is principally garaged in MN shall maintain insurance during the period of operation or use is contemplated.
So it would appear that if your car is registered it needs to maintain insurance on it. It is also garaged (parked) in the state and on a public road so it likely needs to maintain registration and license plates.
You can check with the Minnesota Driver and Vehicle Services to see if there is special registration or insurance that is offered for a vehicle that is non-operational due to being in need of repairs or for other reasons. Some states offer a lower registration rate for inoperable cars.
To maintain insurance on your vehicle as required by MN law, get a quick quote from an Auto Insurance Specialist.