Tex. R. Civ. P. 223
In counties governed as to juries by the laws providing for interchangeable juries, the names of the jurors shall be placed upon the general panel in the order in which they are randomly selected, and jurors shall be assigned for service from the top thereof, in the order in which they shall be needed, and jurors returned to the general panel after service in any of such courts shall be enrolled at the bottom of the list in the order of their respective return; provided, however, after such assignment to a particular court, the trial judge of such court, upon the demand prior to voir dire examination by any party or attorney in the case reached for trial in such court, shall cause the names of all members of such assigned jury panel in such case to be placed in a receptacle, shuffled, and drawn, and such names shall be transcribed in the order drawn on the jury list from which the jury is to be selected to try such case. There shall be only one shuffle and drawing by the trial judge in each case.
Tex. R. Civ. P. 223