It is important to exchange information and call law enforcement for an incident report when an accident has occurred. In many states, it is required of the drivers to make a report if any injuries are sustained and/or if there is property damage above a certain dollar amount.

It is understandable that without auto insurance you might be leery of calling the police but to get your property damages and bodily injuries paid for, a police report will likely be required by the at-fault party's insurance company. Penalties for driving uninsured are something you might face but that is a separate issue from making a claim or police report.

You might be able to call the police and make a report now or in some states the DMV allows you to print off an accident form from online and send it in. With the other person's license plate number, the police or DMV might be able to run a check and give you information on the person so that you can contact them and get their insurance information.

If you live in a 'no-fault' state, personal injuries would typically fall on your insurance company to cover. Since you are without insurance, you would have to check with state regulation to see if there would be another way in which to get your medical bills paid for if you do begin to feel pain from being rear-ended.