You might be able to register a car in Michigan without residency but you will need a state driver's license in most instances to obtain car insurance. To acquire a Michigan State driver's license you need to prove residency but that state does not require you to have a social security number.

It will be very difficult to get auto insurance without having a driver's license from Michigan or another state. There are insurance companies that will allow you to purchase an insurance policy with your international driving permit, as long as you obtain a state driver's license within a certain period of time, usually 30 days.

You can receive a car insurance quote here for the vehicle you are purchasing in Michigan.