How long does a auto insurance have to file a law suit against you for an accident you did not have auto insurance?

Laws vary by state but I can tell you for the state of California you have up to 3 years from the date of the accident to attempt to collect money from the responsible party (ex: filing suit against someone). Now just so you know, if it was confirmed you were not insured on the date of loss, most major companies will just send the file to a collections company to go after you for the money.