Most household and building debris can go in your container. Michigan's landfill rules set the main limits.
The Michigan Department of Environment, Great Lakes, and Energy keeps a list of materials landfills can't take. It includes asbestos, deposit beverage containers, yard clippings, empty drums, hazardous waste, liquids, lead acid batteries, medical waste, PCB waste, scrap tires, septage, and used oil. A landfill can take tires only if they've been cut in half or shredded, and used oil must be recycled.
Grass, leaves, and brush belong at a compost site, not in a mixed dumpster. For appliances with Freon, like freezers and air conditioners, the City asks you to call Public Works. The Isabella Conservation District runs household hazardous waste and electronics collections at 989-772-5927, extension 3.
Paint, solvents, and fuel stay out too. Ask your account manager about anything you're unsure of before you load it.