An owner or lessee of any dwelling containing rooming house accommodations or any room or rooms used for single room occupancy shall keep a register in such dwelling in the custody of a responsible agent. The register shall show: The name, signature, age, previous residence, date of arrival and date of departure of each tenant of rooming house accommodations or of a room or rooms used for single room occupancy; the room or rooms occupied by such tenant; and the names and ages of all persons residing in or occupying such room or rooms with such tenant. The owner or lessee of such a dwelling and the agent who maintains the register in such dwelling shall permit any officer or employee of the department or any inspector from any city department to inspect the register. It shall be unlawful for such owner or lessee knowingly to cause or permit any false entry to be made in such register. It shall be unlawful for any tenant to provide the owner or lessee of such dwelling with any false information on any matter required to be included in the register.