WASHINGTON – The Supreme Court said Thursday that a convicted rapist has no constitutional right to test biological evidence used at his trial in Alaska years earlier, leaving it to the states to decide when prisoners get access to genetic evidence that might prove their innocence.

In a 5-4 vote, with the conservative justices in the majority, the court said it would not second-guess states or force them routinely to look again at criminal convictions.

William Osborne, convicted in a brutal assault on a prostitute in Alaska 16 years ago, sued for the right to test the contents of a blue condom the victim says was used by her attacker. A federal appeals court said he had a right to conduct the test.

Alaska is one of only three states without a law that gives convicts access to genetic evidence. The others are Massachusetts and Oklahoma.

Testing so far has led to the exoneration of 240 people who had been found guilty of murder, rape and other violent crimes, according to the Innocence Project, which works to free people who were wrongly convicted.

But Chief Justice John Roberts, in his majority opinion, said the states have moved quickly to grapple with the challenges and opportunities presented by advances in genetic testing.

"To suddenly constitutionalize this area would short-circuit what looks to be a prompt and considered legislative response," Roberts said.

The chief justice said that new technology that was not available at trial should not throw fairly won convictions into doubt. "The dilemma is how to harness DNA's power to prove innocence without unnecessarily overthrowing the established system of criminal justice," he said.

Dissenting liberal justices and advocates for prisoners who seek genetic testing complained that the court is penalizing a small group of inmates who lack access to a simple test that would conclusively show their innocence, or reaffirm their guilt.

"The fact that nearly all the states have now recognized some postconviction right to DNA evidence makes it more, not less, appropriate to recognize a limited federal right to such evidence in cases where litigants are unfairly barred from obtaining relief in state court," Justice John Paul Stevens said.

Peter Neufeld, a co-founder of The Innocence Project who argued Osborne's case at the Supreme Court, said the ruling probably would not affect the vast majority of inmates seeking DNA testing.

But, Neufeld said, "There is no question that a small group of innocent people — and it is a small group — will languish in prison because they can't get access to the evidence."

The Obama administration, picking up the argument first made by the Bush administration, urged the court to reject the appeals court ruling and insist that inmates at least swear under oath to their innocence before being given access to the evidence. The federal DNA testing law has such a requirement.

In some states, laws limit testing to capital crimes or rule out after-the-fact tests for people who confess.

The woman in Alaska was raped, beaten with an ax handle, shot in the head and left for dead in a snow bank near Anchorage International Airport. The condom that was found nearby was used in the assault, she said.

The woman, who is white, identified Osborne, who is black, as one of her attackers. Another man also convicted in the attack has repeatedly incriminated him. Osborne himself described the assault in detail when he admitted his guilt under oath to the parole board in 2004.

In many exoneration cases, eyewitnesses picked out the wrong man, often with the victim of one race incorrectly identifying someone of a different color.

Osborne's lawyer passed up advanced DNA testing at the time of his trial, fearing it could conclusively link him to the crime. A less-refined test by the state showed that the semen did not belong to other suspects but could be from Osborne, as well as about 15 percent of all African-American men.

Osborne is awaiting sentencing on another conviction, a robbery he committed after his parole.

The case is District Attorney's Office v. Osborne, 08-6.