Most construction and household debris loads without trouble. The limits come from what the receiving facility will take rather than from a statewide list.
Kentucky publishes no single banned-materials table. Instead the state controls disposal by the class of landfill, and construction and demolition material has its own class with its own sites. In practice that means the gate decides, and the gate is strict.
Hazardous waste, liquids, paint, solvents, fuel, used oil, and asbestos must stay out of any container. Tires, vehicle batteries, and refrigerant-bearing appliances need their own route, and so do televisions, monitors, and computers.
Northern Kentucky gives you those routes. The three counties run a joint solid waste program with separate handling for tires, used oil and filters, paint, aerosols, antifreeze, batteries, and prescription drugs, plus an annual household hazardous waste collection event. Electronics, flooring, wood, furniture, plastic foam, and yard debris are all barred from the county recycling bins, so none of those belongs in a bin either.
When something is borderline, ask your account manager before it goes in the container rather than after.