Frequently, but not always, your own car insurance will cover you for any liability incurred while driving a rental car. I would recommend you promptly contact your personal auto insurance company. They will be able to lead you in the right direction.
Please note that I am only licensed in State of Florida and this is for general information purposes only. The first thing I would do is contact my own car insurance company and let the know what happened. Normaly you should have coverage there for any actions in other vehicle that you are in. You can also check with your agent that sold you your policy for your own personal car.
If you have a personal car which was insured at the time of the accident with your rental car, your accident using the rental car may well be covered under your personal auto liability policy as a temporary replacement vehicle. You should consult an attorney in the state where you live to have him or her review your policy.
You should do two things as soon as possible. First contact you own insurance company that has the liability insurance on your personal car to report the accident and send them a copy certified mail of the lawsuit if you have already been served with papers. Your insurance company will then have to advise you in writing if the claims made by the other driver are covered under your own policy. Second you should contact an attorney in your community that can answer the specific questions about money in the bank and other assets since each state has different laws regarding what can happen to your assets in the event of a judgment against you.
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