Actually, there is a very specific law. The backup is a Justice of the Peace, IIRC. The county clerk is required to sign that the license is issued under their personal authority.
The rules for who may have a valid license specifically identify man and woman, and disallow homosexual “marriage”.
OK thanks and you have said that Kentucky law has been ruled invalid by Federal Courts so now there is no law regarding issuance of marriage licenses in Kentucky. Or certainly no law demanding that the county clerk must sign them or issue them