There are 6 US Post Offices in Morgan County serving a total of 13,245 residents equating to 2,208 residents per post office. It's estimated that approximately 21,140 packages are handled across the 6 county post offices annually. Morgan County is a county located in the U.S. state of Kentucky. As of the 2010 census, the population was 13,923. Its county seat is West Liberty. The county is among the dry counties, which means that the sale of alcohol is restricted or prohibited.