State insurance laws and insurance companies' guidelines can differ but normally if you only have liability your insurance company is not involved in your claim against the at fault party's insurance carrier.

If you had collision insurance on your vehicle then your insurance company may be involved in the insurance claims process just in case the other party did not accept the claim and it ended up going through your own coverages.

To find out if your insurance policy states that your insurer will be an advocate if you place an insurance claim with another company read through the terms of the policy. While to find out about state insurance laws you can contact your state's insurance regulator.