The authority to issue an arrest warrant in Austin, Travis County stems from Atricle 15 of the Texas Penal Code. Below, you can find the actual Statutes sections:
Art. 15.01. WARRANT OF ARREST. A "warrant of arrest" is a written order from a magistrate, directed to a peace officer or some other person specially named, commanding him to take the body of the person accused of an offense, to be dealt with according to law.
Art. 15.02. REQUISITES OF WARRANT. It issues in the name of "The State of Texas", and shall be sufficient, without regard to form, if it have these substantial requisites:
1. It must specify the name of the person whose arrest is ordered, if it be known, if unknown, then some reasonably definite description must be given of him.
2. It must state that the person is accused of some offense against the laws of the State, naming the offense.
3. It must be signed by the magistrate, and his office be named in the body of the warrant, or in connection with his signature.
Art. 15.03. MAGISTRATE MAY ISSUE WARRANT OR SUMMONS. (a) A magistrate may issue a warrant of arrest or a summons:
1. In any case in which he is by law authorized to order verbally the arrest of an offender;
2. When any person shall make oath before the magistrate that another has committed some offense against the laws of the State; and
3. In any case named in this Code where he is specially authorized to issue warrants of arrest.
(b) A summons may be issued in any case where a warrant may be issued, and shall be in the same form as the warrant except that it shall summon the defendant to appear before a magistrate at a stated time and place. The summons shall be served upon a defendant by delivering a copy to him personally, or by leaving it at his dwelling house or usual place of abode with some person of suitable age and discretion then residing therein or by mailing it to the defendant's last known address. If a defendant fails to appear in response to the summons a warrant shall be issued.