Most household and construction debris loads without a problem. The limits come from Connecticut's recycling law and from what the Milford Transfer Station will accept at the gate.
Connecticut makes recycling mandatory for residents and businesses alike, and the state says you must not knowingly mix designated recyclables with trash. Scrap metal and appliances, waste oil, car batteries, rechargeable batteries, leaves, mattresses, and covered electronics like TVs, monitors, printers, and computers all have to be kept out of a trash load. Grass clippings and those electronics are banned from disposal outright.
Hazardous waste, liquids, paint, solvents, fuel, and asbestos stay out of a standard container, with no exceptions. Propane tanks are refused too.
The city station also turns away porcelain fixtures, tile, concrete, brick, stone, pavers, asphalt, roofing shingles, and drywall. That does not mean you cannot throw them out, only that the load has to go somewhere else, so flag them when you book.
If an item has you guessing, ask your account manager before it goes in the container.