There are 7 US Post Offices in Duchesne County serving a total of 18,961 residents equating to 2,709 residents per post office. It's estimated that approximately 30,264 packages are handled across the 7 county post offices annually. Duchesne County /du\u02d0\u02c8\u0283e\u026an/ is a county located in the U.S. state of Utah. As of the 2010 census, the population was 18,607. Its county seat is Duchesne, and the largest city is Roosevelt."