Does the U.S. Constitution permit an innocent person to be imprisoned or executed? Seems like a question with an obvious answer.

Here’s another question: If a convict can establish irrefutable proof of his innocence with a simple DNA test, does he have a constitutional right to that test, even if he has exhausted his legal appeals?

The answer to both questions isn’t at all clear, and may depend on how the Supreme Court rules in the case of District Attorney's Office v. Osborne, which it heard today. Surprisingly, 32 states, the city of New York, and the Obama administration are urging the Court to answer "no."

The defendant in the case is William Osborne, who in 1993 was convicted of a brutal kidnapping, rape, and assault in Alaska. DNA testing on semen found in a condom at the crime scene didn't exclude Osborne, but it did include as many as 16 percent of all black men. More sophisticated testing not available at the time of Osborne’s trial would today conclusively determine whether he actually committed the crime. Even the state of Alaska concedes that a negative test would confirm that Osborne is innocent. The test would cost all of $1,000, a fee that would be paid not by the state, but by Osborne’s own legal team at the Innocence Project.

Yet the state of Alaska refuses to hand the sample over for testing, and has fought all the way to the Supreme Court to keep it from Osborne’s lawyers. The state claims that Osborne’s trial produced more than sufficient proof that he committed the crime, and that this is all they need to feel confident in his guilt. Establishing a constitutional right to DNA testing in cases like Osborne’s, the state says, would be wasteful and unnecessary, and undermine the certainty and finality that lends integrity to the criminal justice system. Ken Rosenstein, the state’s lead attorney on the case, told the Anchorage Daily News, "If there was other doubtful evidence that supported his...possible innocence...things might be different. But it's merely a wish and a prayer at this point."

That may well be true. Osborne is hardly a sympathetic character. He was paroled in 2007 for the conviction at issue before the Court. But six months later, he was back in prison after accepting a plea bargain on charges related to a robbery and home invasion. When the Anchorage Daily News pressed to affirm his innocence even in the case now before the Court, he evaded the question.

But the facts of Osborne’s case are in many ways irrelevant—or at least they should be. That Osborne may be a shady character shouldn't allow other states to deny irrefutable DNA testing post-conviction simply because state officials believe that the convictions are rock-solid. Courts and prosecutors have been plenty wrong in the past about even seemingly slam-dunk cases.

Consider the case of Bruce Godschalk, a Pennsylvania man convicted of raping two women in 1986. Godschalk was arrested after his sister thought he resembled a composite sketch of the rape suspect and turned him in to the police. After a long interrogation, Godschalk eventually confessed. In the audio recording of his confession, he recounted 20 details of the rapes that prosecutors said were never released to the public. He was also identified by one of the victims, and a jailhouse informant later claimed Godschalk confessed to him in the cell they shared.

That would seem to be a pretty open and shut case. And indeed, a Pennsylvania court rejected Godschalk’s initial attempt to obtain post-conviction DNA testing on the semen found in the victims, citing the overwhelming evidence of his guilt—including his confession.

Fortunately, a state appeals court relented, and granted Godschalk’s request for testing. Two separate labs later determined that though the same man raped both women, Bruce Godschalk was not that man. As for the details of the crime that he relayed during the confession, that information was actually introduced by his interrogators through suggestive questioning. The jailhouse informant was obviously lying.

One study of DNA exonerations published last year in the Columbia Law Review found 32 cases in which a defendant confessed to a crime for which he was later exonerated. In 16 exoneration cases, an appeals court made reference to the “overwhelming” evidence of the defendant’s guilt in rejecting his appeal.

This isn’t the first time the Supreme Court has entertained the argument that the Constitution prevents the incarceration or execution of the innocent. In the 1993 case Herrera v. Collins, a divided Court denied relief to a Texas man convicted of killing two police officers who claimed new evidence (an affidavit from someone claiming another man confessed to the crimes) conclusively proved his innocence. In the majority opinion, Chief Justice William Rehnquist held that a claim of actual innocence based on evidence discovered after a conviction would need to be “extraordinarily high” to merit a new trial, given the burden such claims would put on the criminal justice system. Herrera’s affidavits, Rehnquist wrote, didn’t meet that standard. In a concurring opinion, Justice Sandra Day O’Connor pointed to the strong evidence of Herrera’s guilt, finding his claim of actual innocence lacking but adding that if someone could prove actual innocence, the Constitution would of course forbid their execution.

Strikingly, in a dissent joined by Justice Clarence Thomas, Justice Antonin Scalia disagreed. Scalia wrote that “there is no basis in text, tradition, or even in contemporary practice (if that were enough) for finding in the Constitution a right to demand judicial consideration of newly discovered evidence of innocence brought forward after conviction.” In other words, the Constitution guarantees only a fair trial and access to an appeal. It doesn't necessarily forbid the execution or incarceration of an innocent person. Once you've exhausted your appeals, Scalia argued, you've exhausted your right to be heard in the courts, even if new evidence could establish your innocence.

The Osborne case, however, is substantially different from Herrera’s in a very important way: This isn’t a matter of an eyewitness recanting his testimony, or a new alibi witness coming forward. Osborne is asking for a test not available at the time of his original trial that will establish beyond all doubt whether he’s innocent or guilty. Surprisingly, the Obama administration's amicus brief (which to be fair, may have been drawn up during the Bush administration) seems to borrow from Scalia's dissent in Herrera. "There is no tradition in this country of granting convicted criminals post-conviction access to the prosecution’s evidence locker, whether for DNA testing, fingerprint analysis, or other purposes," the brief argues. "And constitutional rights do not spring into existence simply because science has advanced."

Currently, Alaska is one of six states that provide no statutory right to post-conviction DNA testing. But while many others have such a right in theory, the laws are written narrowly enough to exclude the vast majority of defendants (many states limit such access to death penalty cases, for example). Some 232 people have been exonerated by DNA testing since 1989. Seventeen had been sentenced to death. In a fifth of those cases, prosecutors fought against allowing the defendant access to evidence for DNA testing.

Every exoneration means not only that an innocent person did time for a crime he didn’t commit, but also that the person who actually committed the crime was allowed to go free. One amicus brief filed on Osborne’s behalf by several former prosecutors (including former U.S. Attorney General Janet Reno) points to several cases in which prosecutors vigorously fought DNA testing for years. When the tests were finally done, they not only cleared the defendant, but when checked against DNA databases they were able to identify the actual culprit. In some cases, the actual culprit escaped justice, because in the time the prosecutors spent blocking the test in the courts, the crime’s statute of limitations had expired. In other cases, the actual culprit passed away. Many times the real culprits went on to commit more crimes.

The anti-Osborne position puts a premium on finality and closure. The landmark case Brady v. Maryland (1963), established that the state is obligated to turn over any exculpatory evidence to defense attorneys before the start of a trial, on the premise that our criminal justice system values uncovering the truth over merely winning convictions. The state of Alaska and its supporters are arguing in Osborne that once a defendant has exhausted his appeals, those values switch, making the protection of a conviction more important than achieving actual justice.

Radley Balko is a senior editor at Reason magazine.