In the US you need to get the FBI/Police records notarized by the state attorneys office and then by a Chinese embassy.
Typically (Ohio) you get the record notarized locally, then get the notary "validated" by the county, then send / carry the document to Columbus (Secretary of State's office) who can affix an Apostile to the document. This all gets sent to the embassy (or consulate) where it is notarized (China) and returned to you. There's a form that has to be filled out and sent with the report, and it has to be sent to a certain consulate (depends of your state of residence). This can all be done in one day if you're willing to drive to Columbus. You might really need somebody with exact details to guide you through the process, though.