Z visa, employment permit, physical examination and no criminal certificate

I am in the process of applying for work Z type to work in China. One of the documents required for it is employment permit.
To apply for employment permit, it's required to have a physical examination in a hospital appointed by the Chinese Embassy. Do you have a list of hospitals in the US appointed by your embassy to conduct the physical examination?

It's also required for no-criminal record. The local police department do not issue no-criminal certificate. What should I do?

Thanks a lot!