If a car backs into you in a MN parking lot a no fault state and there is no police report can you make them pay?

"No fault" in MN means that your own insurance company will pay for your medical expenses and/or wage loss if you are injured in a motor vehicle accident. Even without a police report you can contact the other driver's insurance company and make a claim for your property damage, if you have any. If the person is uninsured you then contact your insurance company to settle the property damage.