Visting HK and China

Hong Kong have a free entry policy. Most people from around the world can enter HK without a visa and thus, not subjected to criminal record checks.
China, on the other hand, requires everyone to have visa. However, they do not require criminal record check either. [http://www.tourismchina-ca.com/visainstruct.htm]
In summary, as long as you are not a fugitive or escaped from lawful custody, you can enter both HK and China as a tourist.