There are 2 US Post Offices in Hancock County serving a total of 8,661 residents equating to 4,331 residents per post office. It's estimated that approximately 13,824 packages are handled across the 2 county post offices annually. Hancock County is a county located in the U.S. state of Kentucky. As of the 2010 census, the population was 8,565. Its county seat is Hawesville. Hancock is a prohibition or dry county. Hancock County is included in the Owensboro, KY Metropolitan Statistical Area."