The judge or clerk of the district court issuing any marriage license shall make a complete record of the application, license, and certificate thereon, on an optical disc, microfilm, microfiche, imaging, in a book kept by the judge or clerk for that purpose, properly indexed, or by electronic means using any method approved by the Supreme Court; and the record of the license shall be made before it is delivered to the person procuring the same, and the record of the certificate shall be made upon the return of the license; provided, that all records pertaining to the issuance of such license shall be open to public inspection during office hours; provided further, that after recording of the original license and completed certificate as hereinbefore required, it shall be returned to the persons to whom the same was issued, with the issuing officer’s certificate affixed thereon showing the book and page or case number where the same has been recorded.