There are 5 US Post Offices in Cleburne County serving a total of 14,416 residents equating to 2,883 residents per post office. It's estimated that approximately 23,010 packages are handled across the 5 county post offices annually. Cleburne County is a county of the U.S. state of Alabama. As of the 2010 census, the population was 14,972. Its county seat is Heflin. Its name is in honor of Major General Patrick R. Cleburne, of Arkansas. The eastern side of the county borders the state of Georgia."