Courthouses in Clinton, Kentucky, the US. Courthouses locations in Clinton, Kentucky. Find the nearest courthouses locations, near you. All types of business services Accounting ATM Bank Courthouse Finance Lawyer School All courthouses in Clinton Circuit Clerk Office Courthouse +1 270-653-3901 109 South Washington Street,, Clinton, Kentucky 42031 Write a review Phone Website Directions County Judge Courthouse +1 270-653-4369 110 West Clay Street, Clinton, Kentucky 42031 Write a review Phone Website Directions