There are 7 US Post Offices in Limestone County serving a total of 22,807 residents equating to 3,258 residents per post office. It's estimated that approximately 36,403 packages are handled across the 7 county post offices annually. Limestone County is a county located in the U.S. state of Texas. As of the 2010 census, the population was 23,384. Its county seat is Groesbeck. The county was created in 1846."