Texas Code of Criminal Procedure - CRIM P Art. 15.19. Notice of arrest

(a) If the arrested person fails or refuses to give bail, as provided in Article 15.18, the arrested person shall be committed to the jail of the county where the person was arrested. The magistrate committing the arrested person shall immediately provide notice to the sheriff of the county in which the offense is alleged to have been committed regarding:

(b) If a person is arrested and taken before a magistrate in a county other than the county in which the arrest is made and if the person is remanded to custody, the person may be confined in a jail in the county in which the magistrate serves for a period of not more than 72 hours after the arrest before being transferred to the county jail of the county in which the arrest occurred.