Tex. Hum. Res. Code § 63.004
The facility shall be governed by a board of trustees. The board of trustees for a facility created by a single county may be the commissioners court of the forming county, or the commissioners court may appoint from the qualified voters of the region to be served a board of trustees consisting of no less than five nor more than nine persons. If the board of trustees is appointed from the qualified voters of the region to be served, the terms of the members thereof shall be staggered by appointing not less than one-third nor more than one-half of the members for one year, or until their successors are appointed, and by appointing the remaining members for two years, or until their successors are appointed. Thereafter, all appointments shall be made for a two-year period, or until their successors are appointed. Appointments made to fill unexpired terms shall be for the period of the unexpired term, or until a successor is appointed.
Tex. Hum. Res. Code § 63.004