There are 6 US Post Offices in Union County serving a total of 4,534 residents equating to 756 residents per post office. It's estimated that approximately 7,237 packages are handled across the 6 county post offices annually. Union County is the northeasternmost county in the U.S. state of New Mexico. As of the 2010 census, the population was 4,549, making it the fourth-least populous county in New Mexico. Its county seat is Clayton. The county was formed in 1894. Union County borders Colorado to the north, and Oklahoma and Texas to the east."