It does, but such things do not usually specify that Mr. Joe Schmoe of 120 Main St in Anytown, RS (Random State) has to die; they're usually more on the order of "we're going to cut funding of <X> even if it means some semi-random people may die." There are acts of war, too, but different rules apply.
In the case from the OT, fortunately, guilt apparently isn't in question. What is in question is how far the prosecution went to put the guy on death row. As I quoted above, it appears that they were willing to use "expert" testimony asserting, basically, that because the defendant is black he's more likely to kill again. It's offensive and, while IANAL, it sounds to me like it shouldn't have been allowed. The fact that the former top lawdog of Texas thinks so too ought to make even the most staunch pro-execution people think twice.