So it turns out there are a number of different kinds of libraries in Ohio. From what I gather, the CH-UH Public Library is a
3375.15 School district free public library, independent of the School District. On that basis, the Library Board would not be permitted to post the park.
There is a non-public school in the building, however, on the same parcel as the park. Does that mean that the entire parcel is a school safety zone? Here's 2923.1212(B):
(B) The following boards, bodies, and persons, 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 Ohio Revised Code section 2923.122, no person shall knowingly possess, have under the person's control, convey, or attempt to convey a deadly weapon or dangerous ordnance into a school safety zone.":
(1) A board of education of a city, local, exempted village, or joint vocational school district or that board's designee in a conspicuous location in each building and on each parcel of real property owned or controlled by the board;
(2) A governing body of a school for which the state board of education prescribes minimum standards under section 3301.07 of the Revised Code or that body's designee in a conspicuous location in each building and on each parcel of real property owned or controlled by the school;
(3) The principal or chief administrative officer of a nonpublic school in a conspicuous location on property owned or controlled by that nonpublic school.
That nonpublic school seems to be allowed to post "property owned or controlled by that nonpublic school". The nonpublic school in this instanced is a tenant (they rent), so they don't own the property. And I don't think they want to claim that they control the park.
Can someone please check my logic and the law? I think I'm back to the beginning: this Library can't post this park.