Being prudent while carrying concealed.
The codes are pretty specific as noted below exempt specific persons from restricted carry and they are not CHL holders, so if you see a sign prohibiting you will need to comply or be in violation of one if not more Ohio Revised Codes.
Lawriter - ORC - 2923.1212 [Effective Until 1/1/2014] Signage prohibiting concealed handguns.
“The following persons, boards, and entities, or designees, shall post in the following locations a sign that contains a statement in substantially the following form: "Unless otherwise authorized by law, pursuant to the Ohio Revised Code, no person shall knowingly possess, have under the person's control, convey, or attempt to convey a deadly weapon or dangerous ordnance onto these premises.":
This shows that the verbiage must be specific to apply to law to the circumstances in order for the law to apply.
Lawriter - ORC - 2923.122 Illegal conveyance or possession of deadly weapon or dangerous ordnance or of object indistinguishable from firearm in school safety zone.
(D)
(1) This section does not apply to any of the following:
(a) An officer, agent, or employee of this or any other state or the United States, or a law enforcement officer, who is authorized to carry deadly weapons or dangerous ordnance and is acting within the scope of the officer's, agent's, or employee's duties, a security officer employed by a board of education or governing body of a school during the time that the security officer is on duty pursuant to that contract of employment, or any other person who has written authorization from the board of education or governing body of a school to convey deadly weapons or dangerous ordnance into a school safety zone or to possess a deadly weapon or dangerous ordnance in a school safety zone and who conveys or possesses the deadly weapon or dangerous ordnance in accordance with that authorization;
(b) Any person who is employed in this state, who is authorized to carry deadly weapons or dangerous ordnance, and who is subject to and in compliance with the requirements of section 109.801 of the Revised Code, unless the appointing authority of the person has expressly specified that the exemption provided in division (D)(1)(b) of this section does not apply to the person.