It isn't in my jurisdiction. By contrast, insanity and duress are affirmative defenses, meaning that to asset the defense the defendant must prove that he was acting while insane or under duress by a preponderance of the evidence. Self defense, if adequately raised by the evidence, must be disproved by the state, but the key is what consititutes adequate evidence to get the self defense question to the jury.
Self defense isn't an affirmative defense here, but the law here is similar to what Northern Piper states. The defendant has the initial burden of producing some evidence to justify submission of a self-defense instruction, and the State must then persuade the jury beyond a reasonable doubt that the defendant did not act in self-defense. Tidmore v. State,976 S.W.2d 724, 729 (Tex.App.–Tyler,1998, pet. ref'd). A bare bones claim that one used deadly force "in self defense" will not likely rise to the level that a self defense instruction should be given to the jury. A defendant merely claiming that they beleived that they were under attack is not enough to warrant the instruction; there has to be some evidence of each of the statutory conditions justifying deadly force. Halbert v. State, 881 S.W.2d 121, 125-26 (Tex.App.–Hous. [1 Dist.],1994, pet. ref'd) Tex.Penal Code Ann. § 9.32 (Vernon Supp.1994). The "some evidence" requirement can conisist solely of the the testimony of the defendant (Id. at 124), but that testimony has to show that if believed it would qualify as a legal justification for the use of deadly force in self defense - merely claiming "it was self defense" won't cut it.
That's not to say that the state should automatically win in the hypo, though; for one thing, they havn't even proven that the death happened within the court's jurisdiction, and the defendant definitely has a claim for ineffective assitance. If the defendant is taking the stand he's doing so in the defense's case in chief, and the fact that the state apparently rested without putting on any evidence means the case should have been unproven had the defendant not testified. The hypo raises some interesting questions about self defense and burdens of proof, but as it stands the only thing we can say for sure that a higher court would do is refer everyone involved to the bar to have their licenses yanked.