If a stillbirth occurs and the stillborn child was delivered under the terms of a gestational agreement entered and validated pursuant to chapter 16, title 7, Idaho Code, then a certificate of stillbirth shall be filed with the bureau of vital records and health statistics according to the provisions of section 39-260(4) and (5), Idaho Code. The certificate shall show the name of the gestational carrier and shall note her status as a gestational carrier. No certificate shall be deemed completed until every item of information required has been provided or its omission satisfactorily accounted for.