Connecticut requires recycling to be kept separate, and Norwalk enforces that at the curb and at the scale. Anything left for collection that contains designated recyclables can be refused by any collector in the city and refused again at the transfer station.
Out of a container entirely: hazardous waste, wet paint, cleaning fluids, acids, caustics, poisons, crankcase and cutting oils, explosives, ammunition, and asbestos. Freon appliances, propane tanks, tires, and batteries all need their own route and have their own fees.
Cardboard, glass and metal food containers, newspaper, office paper, scrap metal, plastics, batteries, waste oil, yard waste, and scrap tires are all on the city's recycling list, which means they should be separated rather than buried in a mixed load.
The city's transfer station adds a construction list that catches people out. It will not take construction and demolition debris, sheetrock, asphalt shingles, ceramic sinks and toilets, or stone and laminate countertops. None of that means you cannot rent a container for a remodel, only that the load has to be routed to a facility that accepts it. Ask your account manager before you load anything you are unsure about.