An uninsured auto accident can put in a very bad spot, even if you are not the person who caused the accident! If you are in California, the "do not pay do not play" law is in effect. If you do not carry liability
insurance, you can not make a claim against the person that hit you. This includes bodily injury and property damage claims! You will be left at your own devices.
If you are not in California, then let me the first one to tell you: stop driving without insurance, go and get yourself a policy, please! You are increasing everyone's premiums. However, this does not mean that insurance companies get a free pass. You need to learn how to protect yourself. You made a huge mistake, no question. Neverheless, you need to learn how to protect yourself so you are not treated unfairly.
Insurance companies do not like people who do not have insurance (either do judges, juries, lawyers, medical providers, nor the public in general). The insurance carrier will try to deny your claim and blame you for the accident. They will put "fault" on you! If the accident is clear (you were later ended), then the insurance company will be more reasonable; however, if the persons that hit you denies or assumes that they did not cause the accident, but you did. Then the insurance company has a duty (not optional) to believe their own client and send you a denial letter. Insurance companies are bound to believe their clients, so if the other driver does not admit fault, it will be up to you to fight back. Since you do not have insurance, you will have to learn the claim process and negotiate as if you were your own insurance adjuster. You need to be ready to settle your uninsured auto accident.
Remember that not having insurance does not mean you caused the accident. You need to separate the two issues and document your claim showing that you had no responsibility in the accident. The first step is to get a copy of the police report. You can go to the Police Records Office and request one. Some jurisdictions will give you a copy the same day. Some others will take up to two weeks. Once you get the police report, make sure you read it thoroughly. Make sure you ask the police records office for an overlay sheet or visit: http://www.auto-insurance-claim-advice.com/overlay-sheet.html to download one from your state.
You need to be looking at what contributor circumstances were attributed to you and the other driver. If there are no codes, or statements made by the officer citing you at fault, then you can point that out to the insurance company.
Read the police report and try to identify witnesses. You can contact them and see if they will be willing to give a statement. Many witnesses will help you if you were really not at fault. Also look at the physical damages left on both vehicles. Is it even possible that the accident happened how the insurance company claims it did?
Write a letter to the insurance company and explain your position. How did the accident happen and what is your evidence. Give them a date line. If they do not answer, then proceed to file a small claims court
lawsuit. Most of the time, insurance companies will try to settle before you go to court. If they do not want to settle, go in front of a judge and explain why you were not at fault. If your case is clear, then the insurance company must pay the judgment.
This is a difficult way to deal with your uninsured auto accident; it would be a lot easier if you had insurance in the first place. If you believe you are being "snowed" by the insurance company, consult with an attorney.