You can if it is related to the job nature of the vacancy. If the criminal record is highly related to the nature of the job, then the employer can ask the job applicant if he has a criminal record.
The Personal Data (Privacy) Ordinance states that personal data for the purposes of which the data are to be used should be collected. No more than that should be collected. There is no expressed rule on what personal data can be collected for each job application. Therefore, this highly depends on the job nature. For instance, if the job includes interacting with children, a sexual conviction record of the job applicant may be required.
