No Passing Zones
Section 3B.02 of the Ohio Manual of Uniform Traffic Control Devices (OMUTCD) states in part "On two-way, two- or three-lane roadways where centerline markings are installed, no-passing zones shall be estiablished at vertical and horizontal curves and other locations where an engineering study indicates that passing must be prohibited because of inadequate site distances or other special conditions." Figure 3B-5 of the OMUTCD gives the method of locating and determining the limits of no-passing zones at curves.
Section 3B.02 of the OMUTCD also makes clear that there is no requirement that no-passing zones be marked at intersections. No-passing zones may be marked at rural and urban intersections when engineering judgment so dictates. The decision as to whether or not a no-passing zone should be marked at intersections is a matter of discretionary engineering judgement. It should be noted that whether or not a no-passing zone is marked at an intersection section 4511.30 of the Ohio Revised Code prohibits vehicles driving on the left side of the road "when approaching within one hundred feet of or traversing any intersection or railroad grade crossing."
The documents linked from this page show where the no-passing zones are marked on state and US routes in ODOT District One.
The ODOT Office of Traffic Engineering has a Centerline Passing and No Passing Logs page that links to no passing zone information for each of the ODOT Districts.