Framing, plaster, sheetrock, shingles, flooring, cabinets, windows, and ordinary cleanout junk all load without trouble. Connecticut's rules are what set the limits, and they are tighter than many people expect.
Recycling is mandatory statewide for households and businesses, and the state names the items banned from disposal: grass clippings, household electronics including televisions, monitors, printers, and computers, and lead-acid or vehicle batteries. None of those belongs in a container.
Paint, mattresses, mercury thermostats, gas cylinders, and tires move through separate statewide programs, so they are declared at booking and handled apart from the main load.
Here is the one with teeth. Connecticut has loads inspected at its waste facilities, and a load carrying a significant share of recyclables can be rejected, with the cost passed down to the customer. Pulling the cardboard and bottles out before pickup is the cheapest insurance on the job.
Hazardous waste, liquids, solvents, and fuel stay out of a standard container as a matter of course. Anything you are unsure about is worth a quick question to your account manager first.