Texas Labor Code - LAB § 102.013. Employee Representation on Board

(a) In a dispute or grievance in which the affected employees are members in good standing of a labor organization:

(b) In a dispute or grievance in which all of the affected employees are not represented by a labor organization, the labor organization in concurrent action with a majority of those employees not represented by a labor organization may designate two arbitrators to serve on the board.

(c) In a dispute or grievance that concerns two or more classes or grades of employees who belong to different labor organizations, the labor organizations in concurrent action may designate two arbitrators to serve on the board.

(d) If the employees concerned in the dispute or grievance are not members of a labor organization, those employees shall call a meeting to elect by majority vote two arbitrators to serve on the board.