The 2020 census found 950 people in the township.

Located in the northern part of the county, it borders the following townships: No municipalities are located in Greene Township.

Starting in 1825 a crossroads settlement named "Greensburg" in the central part of the township had a post office; it was discontinued in 1892.

[6] The township is governed by a three-member board of trustees, who are elected in November of odd-numbered years to a four-year term beginning on the following January 1.

There is also an elected township fiscal officer,[7] who serves a four-year term beginning on April 1 of the year after the election, which is held in November of the year before the presidential election.