It will depend on thee at-fault party's insurance company's guidelines as well as state laws if the police report is enough to get the at-fault party's insurance to get action on your claim. In some states the other party must be contacted in order for the claim to proceed.
In Florida their Department of Insurance states that the insurance company is obligated to pay what the insured is legally liable for because of an accident. A ticket by itself is not evidence of 100%legal liability, therefore, in many instances the company may not have to pay for damages if their insured does not report the accident and cooperation in the investigation. There are many factors taken into consideration when evaluating liability claims. Each situation is judged on its own merit.
In New Jersey if the insurance company does not intend to provide coverage for a loss based on their policyholder’s unwillingness to cooperate, which is a violation of the conditions of the policy, the vehicle and driver are considered to be uninsured for this accident. Under these circumstances you would be able to file an Uninsured Motorist claim with your own company once the other driver’s insurance company denies (disclaims) coverage in writing.
While Washington State notes you cannot force an insured (the person who is named on the insurance policy, also called the policyholder) to file a claim but every insurer, upon receiving notification of a claim, shall respond within ten working days to acknowledge the receipt of such notice unless a payment has been made within that period of time. They also must provide claim forms and help in having their insured report the claim.
Most insurance companies will want to do right and honor a claim if their insured is at fault and responsible for damages to others. Currently you can contact the other party's adjuster and discuss your concerns. He or she should be able to tell you what their rules say will happen if their policyholder continues to ignore them and does not cooperate with the claim.
Also check with your state's insurance regulator to find out what your consumer rights are in this situation. If in yourestate the at-fault party's insurance carrier does not have to accept your claim if their insured does not respond to their inquires, and you do not want to go through your own insurance carrier, you may want to seek legal counsel to see if you can take the at-fault party to court on your own to try and get a judgment for your damages.