Greensburg is a city in Green County, Kentucky, United States. The population was 2,396 at the 2000 census. It is the county seat of Green County. The Downtown Greensburg Historic District is on the National Register of Historic Places and includes the oldest courthouse west of the Allegheny Mountains.
Greensburg is located at 37°15?35?N 85°29?52?W / 37.25972°N 85.49778°W / 37.25972; -85.49778 (37.259665, -85.497863).
According to the United States Census Bureau, the city has a total area of 1.9 square miles (4.9 km²), all of it land.