Normal building debris is fine: framing, plaster, lath, drywall, roofing, siding, flooring, cabinets, porch boards, carpet and cleanout material.
Hazardous material is not. The scales that serve Elmira publish a plain refusal list covering fluorescent bulbs, ballasts, paints other than latex and driveway sealants, and they point people to the Cornell Cooperative Extension on 607-734-4453 for proper disposal of those items. Fuels, solvents, pesticides, acids and free liquids are out as well.
Tires come with conditions rather than a flat ban. The facility requires tires to be clean, dry and off the rims, so pull them out of the load and say so when you book.
Appliances that hold refrigerant are accepted only with the doors off and the units empty, which again is easier to arrange before the container arrives than after it is full.
Elmira's own curbside rules show how narrow the city stream is. Ashes, stones, dirt, furniture, appliances, gas cylinders and yard waste are all on the city's prohibited list for ordinary collection, which is exactly why a container is the right answer for project debris. Anything you are unsure about, ask your account manager first.