Most remodel and cleanout debris is fine. The limits come from the Kentucky Energy and Environment Cabinet, which runs the state Division of Waste Management, and from Elizabethtown's own sanitation rules.
Hazardous waste, liquids, paint, solvents, fuel, used motor oil, and asbestos do not belong in a standard container. Tires, appliances, and electronics have their own routes, and Hardin County runs free collection events through the year for tires, electronic scrap, and household hazardous waste.
Two city rules are worth reading closely. Anything that can be blown away by wind has to be in a covered container, which is a good reason to keep a tarp handy on a windy week. And food waste is treated separately from construction debris here: the city only allows garbage to be hauled in a packer truck approved by its Code Official or the County Solid Waste Officer, so a mixed household load needs a conversation first. A clean load of construction debris or mixed trash is not affected.
Burning waste is a nuisance under city law anywhere in Elizabethtown unless it happens in an approved incinerator, and burning food waste is never allowed. If an item has you unsure, ask your account manager before it goes in the container.