No child care subsidy shall be paid to an unlicensed child care provider if such provider has been convicted of any crime involving sexual assault of a minor or serious physical injury to a minor or any crime committed in any other state or jurisdiction the essential elements of which are substantially the same as such crimes. If the Commissioner of Early Childhood has reason to believe that a provider of child care services has been so convicted, the commissioner may demand that such provider be subject to state and national criminal history records checks. If criminal history records checks are required pursuant to this section, such checks shall be conducted in accordance with section 29-17a.