Ordinary renovation and cleanout debris is fine. Three sets of limits apply, and Dearborn's own list is unusually specific.
Michigan's statewide rules come first. The state environmental agency keeps thirteen categories out of a landfill or treats them as special wastes: asbestos, deposit beverage containers, yard clippings, empty drums, hazardous waste, bulk liquids, lead acid batteries, low-level radioactive waste, medical waste, waste containing PCBs, scrap tires, septage and used oil. Yard clippings have to be composted or taken to a composting facility, and only diseased, infested or invasive-species material may be landfilled. Drums must be full of solid waste or crushed. Bulk liquids from a business have to be solidified first. Tires are accepted only if cut in half or shredded, and used oil must be recycled in Michigan. The agency publishes the whole landfill prohibited materials list.
The City's own refusal list is second and it is longer than most. Dearborn treats as unacceptable waste anything from drums, barrels and explosives through gasoline, kerosene, turpentine, waste oil, batteries, solvents, paints, hydraulic oil, acids and sludge to asbestos, medical waste, ashes of any kind, radioactive material, farm machinery, tar, tires, vehicle bodies and, notably for a yard job, tree stumps or tree limbs over three inches in diameter.
Third is the universal set that applies to any container: no liquids of any kind, no propane or pressurized tanks, nothing hazardous. If you are unsure which group an item falls in, ask your account manager before it goes in.