Most remodeling and cleanout debris is fine. The limits come from Ohio rules and from what the county facility will take.
Ohio EPA is specific about what a municipal solid waste landfill cannot accept: hazardous waste, regulated PCB waste, bulk liquids or waste holding free liquids, untreated infectious waste from a large generator, scrap tires, and yard waste. Those six follow the load wherever it goes.
The Lake County facility names its refusals too, and the list is longer than the state minimum. It will not take out-of-state waste, paints and paint products, chemicals, sprays, pesticides, batteries, automotive fluids, household cleaners, used motor oil, or yard waste of any kind, including brush, stumps, grass, leaves, firewood and bushes.
Tires are a special case here. The county landfill does not bury them. It accepts a small number from residents for a fee and ships them to a scrap tire facility, and anyone generating tires in quantity has to use an approved scrap tire transporter.
Clean concrete, asphalt, brick, block, tile and stone are treated differently again. The Lake County General Health District classes them as clean hard fill that can be reused as construction material, and it asks for written notice at least seven days before any site is filled with it. If your job involves that material, ask your account manager before you plan the load.