To get a police record you will need all of your residents permits for the entirety of your time in China. Without those, you won't be able to get one.
My wife who is a foreigner and we live and work in China, she lost her passport and had to get a new one. When we got the criminal check for China, we could only get the check for the residents permits we had in her new passport. They (NVC) approved our documents and our interview is at the end of the month.
That service that has been mentioned in this thread, send them your scans of all your residents permits and they will be able to get it done for you. If you don't have them, you can't get a criminal check.