In the classification of this question you stated "Criminal record certificate". Although in general, the other suggestions above, "has no criminal record" might work in certain contexts, the official English version of a Hungarian certificate proving that the individual has never been convicted of a crime (büntetlen előéletű) is called the
OFFICIAL CERTIFICATE OF CLEAN RECORD
Issued by the
CENTRAL OFFICE FOR
ADMINISTRATIVE AND ELECTRONIC PUBLIC SERVICES
Whereas the critical lines are as follows:
I HEREBY CERTIFY THAT
(name)
based on the data of the register of criminal records
IS NOT LISTED IN THE REGISTER OF INDIVIDUALS INDICTED UNDER CRIMINAL CHARGES
at her request, I hereby also certify that (s)he is
B1) NOT SUBJECT to any criminal proceedings....
(usually followed by additional statement(s) on (the lack of) restrictions on driving, participating in public affairs, practicing his/her profession, etc.)

If you are translating a Hungarian "Hatósági erkölcsi bizonyítvány", I recommend using the official wording above and not the simplified "no criminal record" version. The latter will suffice if your text is not the actual erkölcsi bizonyítvány but only refers to such certificate.