Ohio Rev. Code § 731.27
Every ordinance or resolution of a legislative authority of a city shall, before it goes into effect, be presented to the mayor for approval. The mayor, if he approves such ordinance or resolution, shall sign and return it forthwith to the legislative authority. If he does not approve it, he shall, within ten days after its passage or adoption, return it, with his objections, to the legislative authority, or, if it is not in session, to the next regular meeting thereof, which objections shall be entered upon its journal. The mayor may approve or disapprove the whole or any item of an ordinance appropriating money. If he does not return such ordinance or resolution within the time limited in this section, it shall take effect in the same manner as if he had signed it, unless the legislative authority, by adjournment, prevents its return. When the mayor disapproves an ordinance or resolution, or any part thereof, and returns it with his objections, the legislative authority may, after ten days, reconsider it, and if such ordinance, resolution, or item, upon such reconsideration, is approved by a two-thirds vote of all the members elected, it shall then take effect as if signed by the mayor.
R.C. §731.27