Tex. Health and Safety Code § 191.026

(a) The local registrar shall secure a complete record of each birth, death, and fetal death that occurs in the local registrar's jurisdiction.

(b) The local registrar shall consecutively number birth and death certificates in separate series, beginning with the number "1" for the first birth and the first death in each calendar year. The local registrar shall sign each certificate to attest to the date the certificate is filed in the local registrar's office.

(c) The local registrar shall copy in the record book required under Section 191.025 each certificate that the local registrar registers, unless the local registrar keeps duplicates under Subsection (d) or makes photographic duplications as authorized by Chapter 201, Local Government Code, or the provisions of Chapter 204, Local Government Code, derived from former Chapter 181, Local Government Code. Except as provided by Subsection (e), the copies shall be permanently preserved in the local registrar's office as the local record, in the manner directed by the state registrar.

(d) The local registrar may permanently bind duplicate reports of births and deaths, if the duplicates are required by local ordinance, and index them in the manner that the state registrar indexes records under Section 191.032.

(e) The local registrar may, after the first anniversary of the date of registration of a birth, death, or fetal death, destroy the permanent record of the birth, death, or fetal death maintained by the local registrar if:

(1) the local registrar has access to electronic records of births, deaths, and fetal deaths maintained by the vital statistics unit; and

(2) before destroying the records, the local registrar certifies to the state registrar that each record maintained by the local office that is to be destroyed has been verified against the records contained in the unit's database and that each record is included in the database or otherwise accounted for.