The U.S. Supreme Court ruled a couple of weeks ago in an Alaska case that it was not a constitutional right to have the most sophisticated DNA applied to crime-scene material after a defendant had already been convicted in what was stipulated to as a fair trial. While the court majority acknowledged the value of DNA, it said the states were evolving standards for its use and it was unnecessary and/or premature for the high court to intervene and dictate standards.
I think I can understand the court's reluctance here, but the argument on the other side is that now that we know how valuable DNA testing can be, it's time to consider such testing part of "due process," which has never been an evolving concept as technology has increased, and the constitution guarantees due process. It wouldn't have been that much of a stretch. The government is rushing to collect DNA from as many people as possible, including in some states people arrested but never charged. It's virtually a standard part of the criminal justice process already. Yet the court shrinks from letting a convict (OK, he was already out on the rape and murder charge and had committed another crime, so he wasn't too sympathetic a character, but the court is supposed abjure sympathy) order and pay for his own test and mandate that the state provide the material with DNA.
This Register editorial, I think, deals with the issue fairly but comes down on the side of as wide a use of DNA as practical in the criminal justice system.