Clinton is a home rule-class city and the county seat of Hickman County, Kentucky, United States. The population was 1,388 at the 2010 cens…Clinton is a home rule-class city and the county seat of Hickman County, Kentucky, United States. The population was 1,388 at the 2010 census, a decline from 1,415 in 2000. Clinton appears to have been named after a riverboat or military captain who was stationed at the location around the time it was settled in the late 1820s. Clinton was incorporated in 1831.