What doI doif the person who causedan accident refuses to turn a claiminto his insurer?

On the police report, it should state the other driver's insurance information.  You could contact that auto insurance company and file your property damage claim.  In addition to paying for the repairs to your car, the at-fault party's insurance carrier should also pay for a rental car while your car is being repaired.  The other party's insurance carrier won't pay for the collision damage waiver on the rental car, but if you have adequate insurance, you won't need it.

Another option would be to sue the at-fault driver for negligence to recover the cost of repairs (property damage) to your vehicle.  You will need to mitigate (minimize) damages by having your car repaired at an auto body shop whose charges are comparable to other auto body shops in the area.  If you selected the most expensive auto body repair shop you could find, your damages (the amount of compensation you are seeking to recover in your lawsuit) would be reduced accordingly.  If you need a rental car while your car is being repaired, you will also need to mitigate damages by selecting a rental car with a reasonable rate.  If you were to select the most expensive rental car you could find, your damages would be reduced accordingly.