There are 10 US Post Offices in Sheridan County serving a total of 4,174 residents equating to 417 residents per post office. It's estimated that approximately 6,662 packages are handled across the 10 county post offices annually. Sheridan County is a county located in the U.S. state of Wyoming. As of the 2010 census, the population was 29,116. The county seat is Sheridan. It is south from the Montana state line. Sheridan County comprises the Sheridan, WY Micropolitan Statistical Area."