Tex. Health and Safety Code § 263.079

(a) A resident of a county in which a county hospital is located who desires treatment in the hospital may apply in person to the superintendent or to a licensed physician for examination. If the physician finds that the resident is sick or injured, the physician may apply to the superintendent for admission of the resident.

(b) After the superintendent receives an application for admission to the hospital, the superintendent shall notify the applicant to appear in person at the hospital if:

(1) it appears from the application that the applicant is sick or injured; and

(2) there is a vacancy in the hospital.

(c) The superintendent, acting under the general direction of the board of managers, shall admit an applicant for admission to the hospital in order of application or according to the urgency of need of treatment if:

(1) after a personal examination of the applicant, the superintendent is satisfied that the applicant is sick or injured; and

(2) the applicant resides in the county at the time of the application for admission to the hospital.

(d) An application for admission must state whether, in the judgment of the physician, the applicant is able to pay, in whole or in part, for the applicant's care and treatment while in the hospital.

(e) An application must be filed and recorded in a book kept for that purpose in the order it is received.