The 2020 census found 1,686 people in the township.

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

Statewide, the only other Elizabeth Township is located in Lawrence County.

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,[4] 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.