High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! Andover Township is one of the twenty-seven townships of Ashtabula County, Ohio, United States. The 2000 census found 2,672 people in the township, 1,403 of whom lived in the unincorporated portions of the township. It is the only Andover Township statewide. 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.