Ohio Rev. Code Ann. § 709.033
(A) After the hearing on a petition for annexation, the board of county commissioners shall enter upon its journal a resolution granting the annexation if it finds, based upon a preponderance of the substantial, reliable, and probative evidence on the whole record, that each of the following conditions has been met:
(C) After the expiration of that thirty-day period, if no appeal has been timely filed under section 709.07 of the Revised Code, the clerk of the board of county commissioners shall take one of the following actions: