I guess that's why the governor released this statement.
Governor Beshear Releases Statement On Clerks Refusing To Issue Marriage Licenses
"Our county clerks took an oath, as elected officials, to uphold the Constitution of the United States and the Constitution of Kentucky and to provide important duties in their communities. This oath does not dictate what our clerks must believe, but it certainly prescribes how they must act in carrying out their duties as elected officials. Same-sex couples in Kentucky are now entitled to the issuance of a marriage license by every county clerk, based on Friday’s ruling by the United States Supreme Court. While there are certainly strongly held views on both sides of this issue, the fact remains that each clerk vowed to uphold the law regardless of his or her personal beliefs. I appreciate the clerks who are fulfilling their duties, issuing licenses to all couples, and I would expect others to execute the duties of their offices as prescribed by law and to issue marriage licenses to all Kentuckians.” reads the statement by Gov. Steve Beshear.