Once you find a 公正行, they will take pictures and will evaluate the cost for maintenace. If you don't know any 公正行, ask your garage operator to see if they could assist to find one for you. Usually, the pirce quote from 公正行 is same as the garage. After that quotation from 公正行 and pictures, you can proceed with the maintenance and no need to wait for statement taken from police.
BTW, before that, you should contact your insurance company / agent and file a report. Depends on the insurance company/agent, you should have it file within 7 days. If not, you will have to bear all the financial involvement.
Some insurance co/agnet will also assist you to claim cost on your behalf (as long as you have reported the accident) but they will charge for a fee, from few hundred to 10% of you actual recieved claim. Usually, the claim for reimbursement will take a lot of time -- a year to a year and half.