That depends on the terms of your insurance policy. If your claim can not be resolved informally you may be able to file a lawsuit in the Superior Court provided that your insurance policy does not require that you submit your case to binding arbitration. Arbitration provisions in insurance contracts are complicated so it is important to retain a qualified lawyer to determine if your policy has an enforceable arbitration clause.
If your policy does require that you submit your case to arbitration your case will be decided by a neutral arbitrator. Your lawyer will gather the evidence and argue your case to the arbitrator who will issue a decision that is binding on you and the insurance company.