On private property, including your own driveway, the Medford ordinances set out no container permit. But Massachusetts is the one state where that answer is incomplete on its own, because the office that matters is the Board of Health rather than the public works department, and its rules are not in the ordinances.
Medford's Health and Human Services Department publishes the list of things it inspects and permits, and two of the entries are ours: the transportation of wastes, and dumpster and trash areas. So the Board of Health is the office with a view on a container here. Its own regulations are kept on file in the city clerk's office rather than published online, which means the terms are a phone call rather than a download. The Board answers on 781-393-2560 and the Director on 781-393-2563, at City Hall Room 311, 85 George P. Hassett Drive. Your account manager will make that call for your address before a container is booked.
The street has a published route. Medford's solid waste rules bar placing and leaving material in any street or public place, naming lumber, building material, earth from cellars, gravel and stone among others, except where the city council or another authorised board or officer of the city permits it. Where a street is obstructed under a permission, the holder must keep a suitable railing or fence around it, lit at night for as long as the obstruction stays, and must repair the street afterwards to the satisfaction of the Director of Public Works.
The sidewalk is close to unusable for a standing container: material may not be left on a footway for more than two hours, and no more than one hour after a public works officer or a police officer asks for it to be moved. For a sidewalk position the City's Engineering Division issues sidewalk occupancy permits, applied for online, with the City Engineer on 781-393-2474. One more detail worth knowing: Medford's own rule says no refuse container may be used unless it is of a type the Director of Public Works has authorised.