Yes you can. If this was a Wisconsin matter, however, you would be found to be violating the mandatory insurance law. But that should not affect your right to sue someone who struck your car. Get your total losses documented (e.g. cost of repairs, medical bills, lost wages, etc.), and make a demand on the other driver, reminding him to notify his insurer. If the insurer will not settle for a reasonable amount in a reasonable time, you can sue. There is a 3-year limitations period within which you can file a lawsuit 3 years from the date of the accident. Surprisingly, 3 years can pass fast, so don't let the grass grow on your claim.
Answered on May 21st, 2015 at 5:10 PM