No. In advisory opinion 2011-038 (2011 Op. Att'y Gen. No. 038), the Ohio Attorney General (OAG) concluded that a public body (in this instance the State Board of Education) may not vote in an open meeting by secret ballot. The OAG determined that voting by secret ballot would violate Ohio's open meetings law in much the same way as a violation occurs when public officials whisper or pass documents among themselves during meetings or when a vote would improperly be taken during executive session. In such situations, a violation occurs because members of the public are prevented from knowing a critical part of the public body's decision-making process.
A copy of the advisory opinion is available for download at the following link: OAG 2011-038