A person receiving specialized services from a local specialized program which receives financial assistance through the department shall be responsible for the cost of such services in the same manner as are persons receiving services at the Beatrice State Developmental Center. Provisions of law in effect on September 6, 1991, or enacted after such date relating to the responsibility of such persons and their relatives for the cost of and determination of ability to pay for services at the center shall also apply to persons receiving services from specialized programs.