Texas law does not make that unlawful.
Here are your Katy city ordinances; Franklin Legal Publishing
ARTICLE 7.200 DISCHARGE OF FIREARMS, AIR RIFLES AND OTHER PROJECTILES PROHIBITED*
It shall be unlawful to discharge any firearm, air rifle, pellet gun, BB gun, carbon dioxide (CO2) gun, bow, crossbow, or so-called hunting slingshot so that the projectile therefrom crosses any public property, or crosses any thoroughfare or property line within the City of Katy, Texas; except that such may be discharged by any party upon his own property and upon the property of another only when acting in such other person's presence and with permission.
You should read Texas law regarding protection of animals. Google Texas Penal Code
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