That depends on whether it’s a misdemeanor or a felony. First and Second Offense DWIs in Texas are Class B, and Class A Misdemeanors, respectively. Third Offense DWI (and above) are Felonies.
Chapter 12 of the Texas Code of Criminal Procedure covers all of the limitations periods for prosecution in Texas.All misdemeanors in Texas have a 2 year statute of limitations, including DWI. Felony DWIs fall under the “regular” 3 year statute of limitations.