I was the victim of a hit and run auto accident. Found out later that the car had been stolen from another city, what can I do.

If this ocurred in Ohio, I would recommend going through your own auto insurance company. Let them repair your vehicle and let them use their own lawyer to sue the person who stole the car.

The owner of the stolen vehicle and his/her insurance carrier are probably not liable if the car was truly stolen.

The answer to your question depends on what you want.

Do you want your car repairs paid? If yes, then you'll have to goto your own insurance company. You can only seek up to $500 from the other party (mini-tort).
Read about this here: http://www.michiganautolaw.com/nofault/michigan-mini-tort.php

Do you want your medical bills or time missed from work paid? If yes, again, you'll have to goto your own insurance company to get PIP benefits.
Read about this here: http://www.michiganautolaw.com/caraccidents/caraccidentbenefits.php

Do you want to recover for pain and suffering for your injuries? If yes, then its unlikely recover anything from the insurance company of a stolen car or the theft himself. Your best method for recover is through your own insurance company if you had purchased Uninsured Motorist Coverage.
Read about this here: http://www.michiganautolaw.com/caraccidents/uninsured-motorist-coverag/index.php

As you can see, your question brings up many more questions from me. I would recommend you seek the advice of an attorney as soon as possible to ensure you don't miss any statute of limitation deadlines.

Good Luck to you,
/Thomas James