There are 8 US Post Offices in Harrison County serving a total of 14,280 residents equating to 1,785 residents per post office. It's estimated that approximately 22,792 packages are handled across the 8 county post offices annually. Harrison County is a county located in the U.S. state of Ohio. As of the 2010 census, the population was 15,864, making it the fifth-least populous county in Ohio. Its county seat is Cadiz. The county is named for General William Henry Harrison, who was later President of the United States.