Texas Health and Safety Code - HEALTH & SAFETY § 191.034. Notation of Death on Birth Certificate

(a) On receipt of the death certificate of a person whose birth is registered in this state, the state registrar shall conspicuously note the person's date of death on the person's birth certificate.

(b) The state registrar shall notify the county clerk of the county in which the person was born and the local registrar of the registration district in which the person was born of the person's death.  On receipt of the notification of death, the county clerk or local registrar shall conspicuously note the person's date of death on the person's birth certificate.