1. Prefectures, etc. (meaning prefectures and designated cities, cores cites as designated under the Local Government Law, Article 252-22-1 [hereinafter, "core cities"] and other cities as designated by law [including special districts, hereinafter: the same]) are required to take custody of dogs or cats when so required by their owners. In such cases, prefectural governors, etc. (including mayors of designated cities, core cities and other cities as designated by law [hereinafter: the same]) may designate the places at which the dogs or cats are to be taken into custody.