I would not recommend speaking with your insurance company unless the other driver refuses to pay for the damages. Because you have the police report and hopefully the other driver's insurance information, you should call their insurance company and begin the claim's process. If you do not have their insurance information, you may call your insurance company's claims department and they should be able to track down the at-fault party for you. The police report should help you with this. Because the other driver is liable for the accident, you won't have to pay your deductible. It will be covered through their liability insurance.
For more resources on how to file a claim, see our article here.