There are 1 US Post Offices in Crockett County serving a total of 3,693 residents equating to 3,693 residents per post office. It's estimated that approximately 5,894 packages are handled across the 1 county post offices annually. Crockett County is a county located on the Edwards Plateau in the U.S. state of Texas. As of the 2010 census, its population was 3,719. The county seat is Ozona. The county was founded in 1875 and later organized in 1891. It is named in honor of Davy Crockett, the legendary frontiersman who died at the Battle of the Alamo."