There isn't some statewide rule though. And not all CCs qualify. I believe each school makes their own agreements. And it doesn't apply to only Public schools.
For example, in Dayton we have a phenomenal CC (Sinclair) and you can attend your first 2 years there and transfer directly into certain schools as a Junior. Some of those schools are:
Miami of Ohio (Public)
Wright State University
University of Dayton (Private)
Ohio University (Public)
And your yearly tuition at Sinclair? A whopping $4k.
It's almost a no brainer if you live in SW Ohio and are considering any of those schools. It's one of the reasons why having the government pay for college. When opportunities like this exist, ANYONE can afford college. Anyone.