All districts
Birmingham does not permit accessory dwelling units. The term accessory dwelling appears nowhere in the zoning ordinance, and § 4.02 AS-01 affirmatively prohibits residential occupancy of accessory buildings in the residential districts.
The single exception is the MX district, where residential units in accessory structures are permitted (§ 4.07 AS-06). The closest residential allowance elsewhere is renting of rooms to at most 2 roomers per dwelling (§ 5.02(D)).
A second dwelling unit on a single-family lot would need a rezoning or use-type relief. These are findings drawn from the ordinance's silence and its prohibition; confirm them with the Planning Division before making plans.