There are 3 US Post Offices in Converse County serving a total of 13,751 residents equating to 4,584 residents per post office. It's estimated that approximately 21,948 packages are handled across the 3 county post offices annually. Converse County is a county located in the U.S. state of Wyoming. As of the 2010 census, the population was 13,833. Its county seat is Douglas."