There are 3 US Post Offices in Green County serving a total of 10,381 residents equating to 3,460 residents per post office. It's estimated that approximately 16,569 packages are handled across the 3 county post offices annually. Green County is a county located in the U.S. state of Kentucky. As of the 2010 census, the population was 11,258. Its county seat is Greensburg. Green is a prohibition or dry county."