Among all of Kentuckyâs 120 counties, Logan County has the stateâs second lowest unemployment rate, according to the latest statistics released last week by the Kentucky Center for Statistics (KYSTATS), an agency of the Kentucky Education and Workforce Development Cabinet. In December, the jobless rate in Logan County was just 4.1%. Only neighboring Todd County had a lower rate at 4.0%. Since Todd County is part of a different district, Logan County also had the lowest rate among the 10-county Barren River Area Development District. Monroe County had the second lowest rate at 4.4% and Allen County came in at 4.8%. Other neighboring Kentucky counties included Warren (5.3%), Simpson (4.9%), Butler (5.6%) and Muhlenberg (7.7%).