Texas Health and Safety Code - HEALTH & SAFETY § 287.041. Board of Directors

(a) A county or hospital district that creates the district and has a population of 125,000 or more shall appoint one director to the board for every 125,000 persons in the population of the county or hospital district, rounded to the nearest 125,000.

(b) A county or hospital district that creates the district and has a population of less than 125,000 may appoint one director to the board.

(c) The county judges of a county that creates the district shall appoint the directors to the board on behalf of the county.  The board of directors of a hospital district that creates the district shall appoint the directors to the board on behalf of the hospital district.

(d) Directors serve staggered two-year terms, with as near as possible to one-half of the directors' terms expiring each year.

(e) The number of directors appointed to the board by each county or hospital district that creates the district is determined at the time of the initial appointment of directors under this section and does not vary with subsequent variations in the population of the county or hospital district.