You are looking for an option that includes three factors: a check of criminal records that leads to a certificate of clearance. So any phrase that includes all three will be understandable by anyone who reads English in any country.
However, as you have realised, the exact phrase used in countries that carry out such checks will differ from one authority to another. And there may be different levels of checking - in Britain for instance, is it a check for any criminal record, or those specifically related to offences against children? So you see why there is no single answer.