The Hong Kong police website states that a criminal clearance letter will only be approved in connection with a person's application for a visa to visit, study or reside in another country, or for adoption of children. However, there is a vague reference to also providing this service when a letter is provided from the relevant Consulate / Immigration Authority / Government Authority, which contains his or her name and clearly indicates that the production of the Certificate is required.
I needed a criminal clearance letter for reasons other than immigration or adoption and was successful in obtaining it.
Contact the notary section of your consulate in Hong Kong and request a letter from the consulate to the Hong Kong police asking for the criminal reference clearance check. Download the application for a criminal clearance check from the Hong Kong police website. Take the consulate letter and completed application to the the Hong Kong Police Headquarters located at 1 Arsenal Street, Wan Chai.
The clearance letter will be sent to your consulate and then forwarded to you.