A public hospital agency may enter into agreements with other hospital agencies, or with homes providing skilled nursing care which are licensed as nursing homes under Chapter 3721 of the Revised Code, to provide or arrange for extended care services to patients of a hospital of such public hospital agency when such services are medically appropriate for them. Such agreements may require such extended care services to be provided under the supervision of the professional staff of the hospital of such public hospital agency or, where such facility in which the extended care is to be provided has an organized medical staff, for transfer arrangements with the hospital of such public hospital agency, or may make other arrangements to assure adequate extended care services for such patients.