Greensburg Township is one of the fifteen townships of Putnam County, Ohio, United States. The 2020 census found 1,427 people in the township.

Putnam County is a county located in the northwestern part of the U.S. state of Ohio. As of the 2020 census, the population was 34,451. Its county seat is Ottawa. The county was created in 1820 and later organized in 1834. Its name is in honor of Israel Putnam, a colonial officer in the French and Indian War, who served as a general in the American Revolutionary War. The Blanchard River, which passes through the county, was a key transportation route for early European-American settlers.