All the parks are ran by Columbus. I emailed Columbus Recreation and Parks Department and this is what they said.
"We do not check the ice thickness and therefore always consider it unsafe. You can certainly fish from the banks of any of our ponds, but entering the pond or waterway is unsafe.
Thank you,
--CRPD 9.14 Fishing. No person shall: (A) Engage in fishing in violation of Ohio R.C. Chapter 1533. (B) Bowfish except on Hoover Reservoir north of the second bridge upstream from the dam. (C) Use nets, buckets, or methods other than pole fishing to harvest fish from ponds which are solely contained within park boundaries, except Antrim Lake.