The state shall pay to the state psychiatric hospital, out of any moneys in the state treasury not otherwise appropriated, all expenses for the administration of the hospital, and for the care, treatment, and maintenance of committed and voluntary public patients in the state psychiatric hospital, including clothing and all other expenses of the hospital for the public patients. The bills for the expenses shall be rendered monthly in accordance with rules agreed upon by the director of the department of administrative services and the state board of regents.