State laws differ or may not even be written regarding this situation but it is not unusual for the insurance company or private party that is taking care of damages out of pocket to request that 3 estimates be done on the damaged vehicle so that they can determine what the repair costs will be.

By receiving 3 estimates you should hopefully see 3 quotes that are relatively close together and so know that you are not paying too much or too little (in that there may be more wrong with the car then the lowest estimate has determined).

These are only guidelines though and many states do not have a requirement or law about how many estimates are required when negotiating the repair of a car when you are a private party paying for an at fault accident.

You may try checking with such state entities as your Department of Motor Vehicles or insurance regulator to see if there are any state laws that govern this situation. For example in Minnesota there are guidelines that insurance companies must follow. In MN your insurance company cannot require you to have your vehicle repaired at a specific repair shop. You may choose your own repair shop; however, the insurance company may require you to have one or more estimates, and if your shop is not the low bidder, you may be responsible for paying the difference.

More than likely if you do not agree with the high estimate and the person will not agree to getting other estimates done you will have to continue to negotiate with them with regards to the cost of repairs.

If you truly believe the costs of repairs are exorbitant then you may decide to let the other party take you to court and prove that the costs of repairs to the vehicle were that expensive. That would be a personal choice to make though. Or you may decide to let the person place a claim through your property damage liability coverage and let your insurance company take over the repairs of the vehicle that was damaged by you in your fender bender.