* DNA tests exonerated at least 232 people nationwide

* Four states do not allow such testing

WASHINGTON, June 18 (Reuters) - Convicted criminals do not have a constitutional right to obtain access to a state’s biological evidence to conduct DNA testing when pursuing claims of innocence, the U.S. Supreme Court ruled on Thursday.

By a 5-4 vote, the nation’s highest court refused to create a new legal right for post-conviction DNA testing, which has exonerated at least 232 people nationwide years after they had been found guilty.

Forty-six states and the federal government have laws that give convicts some access to DNA testing, according to the decision. The ruling was a victory for Alaska, one state that does not explicitly allow such testing, along with Alabama, Massachusetts, and Oklahoma.

States opposed to the testing have said it would be costly and would result in unnecessary litigation in cases in which a defendant received a fair trial and there was overwhelming evidence supporting a guilty verdict.

The justices overturned a U.S. appeals court ruling for William Osborne, who was convicted for the 1993 rape, kidnapping and assault of a prostitute near the Anchorage airport.

The appeals court had ruled that Osborne has a right to subject certain biological evidence to advanced DNA testing as part of his later claims of innocence.

Osborne had waived his chance for the advanced DNA test at trial and later admitted his guilt under oath to a parole board in 2004. Another man also convicted in the attack has repeatedly said Osborne took part in the crimes.

Osborne’s lawyers had decided not to pursue the more advanced DNA testing before his trial, fearing the results might incriminate him. A less refined test by the state showed the biological evidence could be from Osborne as well as about 15 percent of all black men.

Osborne had sought access to the biological evidence for the advanced DNA testing in an effort to prove his innocence.

The U.S. Justice Department supported Alaska and said a right to post-conviction DNA testing would “open the floodgates” for lawsuits seeking new tests for old evidence. It said the issue was best left to the states and Congress to adopt their own procedures.

Writing the opinion for the court’s conservative majority, Chief Justice John Roberts agreed and said rules and procedures are being shaped by legislatures and state courts. “There is no reason to constitutionalize the issue,” he wrote.

Liberal justices John Paul Stevens, David Souter, Ruth Bader Ginsburg and Stephen Breyer dissented. Stevens said there was no reason to deny access to the evidence and cited “a fundamental concern in ensuring that justice has been done in this case.” (Editing by Alan Elsner)