It is named for Dr. Benjamin Rush, an early physician and Founding Father of the United States.

[4] Statewide, other Rush Townships are located in Champaign and Tuscarawas counties.

Rush Township was organized June 3, 1867 by Levi Kirkendall.

[5] 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,[6] 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.