Do cities or villages have any specific authority to reserve parking spaces for physically disabled persons?

Yes. Section 349.13(1m) of the Wisconsin Statutes authorizes a city or village to prohibit use of “any portion of a street, highway or parking facility reserved for any vehicle bearing special registration plates” issued to physically disabled persons under several related statutes or “a motor vehicle, other than a motorcycle, upon which a special identification card issued” to a physically disabled person is displayed or “any vehicle registered in another jurisdiction and displaying a registration plate, card or emblem issued by the other jurisdiction which designates the vehicle as a vehicle used by a physically disabled person.”