Tex. Code Crim. Proc. art. 16.14
After examining the witness in attendance, if it appear to the magistrate that there is other important testimony which may be had by a postponement, he shall, at the request of the prosecutor or of the defendant, postpone the hearing for a reasonable time to enable such testimony to be procured; but in such case the accused shall remain in the custody of the proper officer until the day fixed for such further examination. No postponement shall take place, unless a sworn statement be made by the defendant, or the prosecutor, setting forth the name and residence of the witness, and the facts which it is expected will be proved. If it be testimony other than that of a witness, the statement made shall set forth the nature of the evidence. If the magistrate is satisfied that the testimony is not material, or if the same be admitted to be true by the adverse party, the postponement shall be refused.
Tex. Code Crim. Proc. § 16.14