There are 6 US Post Offices in Clark County serving a total of 16,767 residents equating to 2,795 residents per post office. It's estimated that approximately 26,762 packages are handled across the 6 county post offices annually. Clark County is a county located in the southeastern part of U.S. state of Illinois, along the Indiana state line. As of the 2010 census, the population was 16,335. Its county seat is Marshall. The county was named for George Rogers Clark, an officer who served in the American Revolution.