You can request information from the police about the other person’s auto insurance, but there has to be a legitimate reason for it. An accident, for example, is a valid reason, but you’ll need to have their license plate number and the incident report ready to give to the police officer.
You can also try contacting your local DMV. They will know if a car’s tax has been paid. You’ll need to give your contact information as well as the reason for the request. If you falsify your information, the DMV may reject your request.
If you’re looking into this information as a result of an accident, you’ll also want to inform your car insurance company of both the accident and the lack of information for the other driver; it will help your company know how to process your accident claim.