The 2020 census reported 2,014 people living in the township.

The village of Martinsville is located in northern Clark Township.

Statewide, other Clark Townships are located in Brown, Coshocton, and Holmes counties.

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.

The trustees and clerk are chosen in non-partisan elections.