Actually, it only applies to evidence containing biological material. It can be found in Texas Code of Criminal Procedure
Article 38.43 (it was renumbered, but the courts and lawyers all know what Article 38.39 rights refer to).
It is not targeted at you specifically, though, but does apply to all cases where there is some sort of biological material (this can be blood samples for a DWI, semen samples, heck even a fingernail or piece of hair, so long as it is "biological"). This is a common motion and notice, so don't worry about it.
Here's the statute so you can better understand what rights you have.
Art. 38.43. PRESERVATION OF EVIDENCE CONTAINING BIOLOGICAL MATERIAL. (a) In a criminal
case in which a defendant is convicted, the attorney representing the state, a clerk, or any other officer in possession of evidence described by Subsection (b) shall ensure the preservation of the evidence.
(b) This article applies to evidence that:
(1) was in the possession of the state during the prosecution of the case; and
(2) at the time of conviction was known to contain biological material that if subjected to scientific testing would more likely than not:
(A) establish the identity of the person committing the offense; or
(B) exclude a person from the group of persons who could have committed the offense.
(c) Except as provided by Subsection (d), material required to be preserved under this article must be preserved:
(1) until the inmate is executed, dies, or is released on parole, if the defendant was convicted of a capital felony; or
(2) until the defendant dies, completes the defendant's sentence, or is released on parole or mandatory supervision, if the defendant is sentenced to a term of confinement or imprisonment.
(d) The attorney representing the state, clerk, or other officer in possession of evidence described by Subsection (b) may destroy the evidence, but only if the attorney, clerk, or officer by mail notifies the defendant, the last attorney of record for the defendant, and the convicting court of the decision to destroy the evidence and a written objection is not received by the attorney, clerk, or officer from the defendant, attorney of record, or court before the 91st day after the later of the following dates:
(1) the date on which the attorney representing the state, clerk, or other officer receives proof that the defendant received notice of the planned destruction of evidence; or
(2) the date on which notice of the planned destruction of evidence is mailed to the last attorney of record for the defendant.
(e) To the extent of any conflict, this article controls over Article 2.21.
Added by Acts 2001, 77th Leg., ch. 2, Sec. 1, eff. April 5, 2001.
Renumbered from Code of Criminal Procedure, Art/Sec 38.39 by Acts 2005, 79th Leg., Ch. 728, Sec. 23.001(8), eff. September 1, 2005.