There are 14 US Post Offices in Independence County serving a total of 34,799 residents equating to 2,486 residents per post office. It's estimated that approximately 55,543 packages are handled across the 14 county post offices annually. Independence County is a county located in the U.S. state of Arkansas. As of the 2010 census, the population was 36,647. The county seat is Batesville. Independence County is Arkansas's ninth county, formed on October 20, 1820, from a portion of Lawrence County and named in commemoration of the Declaration of Independence. It is an alcohol prohibition or dry county. The Batesville, AR Micropolitan Statistical Area includes all of Independence County."