Your claim is against the towing company, not its insurance company. If you can't or won't hire a lawyer, the way to proceed is to write a demand letter to the towing company. They will probably notify their liability insurer about your claim. An adjuster should then contact you and ask you about the facts and for documentary evidence of your property damage. After that, the insurer will either negotiate with you or deny your claim. If you are unable to negotiate a settlement with the insurer, your only remedy is through suing the towing company. If the towing company ignores your demand letter, again, your remedy is to sue the towing company.
If you had collision and/or comprehensive coverage of your own on your car, you should make a claim against your own insurer. This is first party, no-fault insurance, so you would not have to prove that anyone was at fault in order to get your insurer to honor your claim.
I agree with my colleagues. You will have difficuly gettting the tow truck compnay to play ball as that is simply the nature of the towing industry. Hire an attorney to write the correct sort of letter initiating a claim for your property damage and be prepared to file a lawsuit to receive your just compensation.
In no way am I offering you legal advice, and in no way has my comment created an attorney-client relationship. You are not to rely upon my note above in any way, but insted need to sit down with counsel and share all relevant facts before receiving fully-informed legal advice. If you want to be completely sure of your rights, you must sit down with an experienced criminal defense attorney to be fully aware of your rights.
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