The superintendent shall admit to the hospital a person sent by the commissioners court of an adjacent county if:
(1) the adjacent county has contracted with the board of managers for the care and treatment of persons who are sick or injured;
(2) the person resides in the adjacent county at the time of the application for admission to the hospital; and
(3) there is sufficient provision for the care of persons who are sick or injured and who reside in the county in which the hospital is located.