Washington Township is one of the eighteen townships of Monroe County, Ohio, United States. As of the 2020 census, the population was 429, including 70 people in the village of Graysville. The village of Graysville is located in northern Washington Township, and the unincorporated community of Rinard Mills lies along the Little Muskingum River in th…Washington Township is one of the eighteen townships of Monroe County, Ohio, United States. As of the 2020 census, the population was 429, including 70 people in the village of Graysville. The village of Graysville is located in northern Washington Township, and the unincorporated community of Rinard Mills lies along the Little Muskingum River in the township's southwest.