There are 4 US Post Offices in Butte County serving a total of 10,306 residents equating to 2,577 residents per post office. It's estimated that approximately 16,450 packages are handled across the 4 county post offices annually. Butte County is a county located in the U.S. state of South Dakota. As of the 2010 census, the population was 10,110. Its county seat is Belle Fourche. The county was established in the Dakota Territory on March 2, 1883, and given the descriptive name based on the French word for a hill."