I visited Burr Oak State Park a week ago, and I saw a sign for Natural Resources Route 10:
(https://upload.wikimedia.org/wikipedia/commons/7/72/Ohio_DNR_Route_10.jpg)
I looked for more info on either the route or the system, and I confirmed that DNR Route 10 appears on the park map (https://dam.assets.ohio.gov/image/upload/ohiodnr.gov/documents/parks/parkmaps/burroakparkmap.pdf), but I couldn't find much more about the DNR routes in general. Does anyone else know more about this system and the routes in it?
Yes, they are statewide and seemingly random (I'm sure there is a system to it but I am not sure how they are numbered) They are also found in Headlands State Park at the north end of OH 44 for example.https://www.google.com/maps/@41.7552643,-81.2883902,3a,15y,247.25h,81.68t/data=!3m7!1e1!3m5!1s5-RPtgdchTz_iooYSK2XTg!2e0!6shttps:%2F%2Fstreetviewpixels-pa.googleapis.com%2Fv1%2Fthumbnail%3Fcb_client%3Dmaps_sv.tactile%26w%3D900%26h%3D600%26pitch%3D8.31678100182755%26panoid%3D5-RPtgdchTz_iooYSK2XTg%26yaw%3D247.2534167422983!7i13312!8i6656?entry=ttu&g_ep=EgoyMDI1MDkwMy4wIKXMDSoASAFQAw%3D%3D
Also in north central Ohio, Mohican State Park has markers. https://www.google.com/maps/@40.60536,-82.3041458,3a,15y,205.48h,88.94t/data=!3m7!1e1!3m5!1sK4-xDHFucibvMRmWrpfETg!2e0!6shttps:%2F%2Fstreetviewpixels-pa.googleapis.com%2Fv1%2Fthumbnail%3Fcb_client%3Dmaps_sv.tactile%26w%3D900%26h%3D600%26pitch%3D1.062826162935977%26panoid%3DK4-xDHFucibvMRmWrpfETg%26yaw%3D205.478808185129!7i16384!8i8192?entry=ttu&g_ep=EgoyMDI1MDkwMy4wIKXMDSoASAFQAw%3D%3D
Various parks in Southeast Ohio (Hocking Hills) but I do not recall which roads I spotted them on