The 2020 census reported 2,711 people living in the township.

[4] It takes its name from Greene County, Ohio.

[5] It is one of sixteen Green Townships statewide.

[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.