Ordinary renovation debris is fine. The exceptions come from state law and from what the receiving facilities refuse.
Hazardous material is the firm line: paint, solvents, fuels, motor oil, pool and garden chemicals, pesticides, aerosols, and anything corrosive. Liquids of any kind and asbestos are out too.
Several common items are handled separately rather than buried. Tires, appliances, batteries, fluorescent bulbs, and electronics all need their own route, and the City's own collection site turns away shingles, tires, appliances, batteries, ammunition, explosives, and medical waste at the gate.
That site is also closed to trade waste. It serves Carmel households only, with photo identification, so a contractor working here has to plan a different path for those materials.
When something falls in a gray area, ask your account manager before it goes in the container rather than after.