Health and Safety Code §263.041

(a) The commissioners court of a county shall appoint at least six but not more than 12 residents of the county as the board of managers of a county hospital or medical or other health facility after the court acquires the site for the hospital and awards the contracts for the buildings and improvements necessary for the hospital. (b) A manager is appointed for a term of two years except that the commissioners court may set the terms of the initial managers at less than two years so that as close as possible to one-half of the managers' terms expire each year. (c) An appointment to fill a vacancy is for the unexpired term. (d) A vacancy is created if a manager misses three consecutive board meetings unless the board takes formal action to excuse the absences.