Greensburg is a city in and the county seat of Decatur County, Indiana, United States. The population was 12,312 at the time of the 2020 cen…Greensburg is a city in and the county seat of Decatur County, Indiana, United States. The population was 12,312 at the time of the 2020 census. Greensburg founder Thomas Hendricks Sr.'s wife named the city in honor of her native town, Greensburg, Pennsylvania. Its first post office opened in 1823 and spelled the city's name as Greensburgh until 1894.