There are 5 US Post Offices in Greene County serving a total of 40,098 residents equating to 8,020 residents per post office. It's estimated that approximately 64,001 packages are handled across the 5 county post offices annually. Greene County is a county located in the U.S. state of Arkansas. As of the 2010 census, the population was 42,090. The county seat is Paragould, which sits atop Crowley's Ridge. Greene County comprises the Paragould, AR Micropolitan Statistical Area, which is also included in the Jonesboro\u2013Paragould, AR Combined Statistical Area."