There are 8 US Post Offices in Green County serving a total of 36,932 residents equating to 4,617 residents per post office. It's estimated that approximately 58,948 packages are handled across the 8 county post offices annually. Green County is a county located in the U.S. state of Wisconsin. As of the 2010 census, the population was 36,842. Its county seat is Monroe. Green County is included in the Madison WI Metropolitan Statistical Area."