You should always report your car accident to your own insurer. Many insurance companies state in the policy documents that you must contact them following an accident. Beyond this, it could turn out that the driver who hit you is uninsured or underinsured, meaning you will have to depend on the uninsured/underinsured motorist coverage on your own insurance policy (if you have this coverage). In some cases, if you are waiting for the other driver’s insurance to pay for the repairs to your car, you may be able to arrange to have your car repaired by using your own insurance, and they will be repaid by the at fault insurance company.