Technically yes, but they are only available in a limited number of cases. Under Texas law (Tex. Civ. Prac. & Rem. Code Ann § 41.001(5)), punitive damages are known as exemplary damages. They are awarded as “a penalty or by way of punishment but not for compensatory purposes.”
However, for the most part, personal injury damages in Texas are designed to be compensatory in nature. Punitive damages could potentially be available in a narrow set of cases, such as with a DUI crash. If you have any specific questions or concerns about punitive damages, contact a Houston car accident lawyer for help.