Greensburg is a home rule-class city in and the county seat of Green County, Kentucky, United States. The population was 2,163 at the 20…Greensburg is a home rule-class city in and the county seat of Green County, Kentucky, United States. The population was 2,163 at the 2010 census, down from 2,396 at the 2000 census. The Downtown Greensburg Historic District is on the National Register of Historic Places and includes the oldest courthouse west of the Allegheny Mountains.
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