WASHINGTON (CNN) -- A convicted rapist seeking to prove his innocence with a new DNA test lost his appeal Thursday at the Supreme Court. 

The U.S. Supreme Court case involved a crime in which post-conviction DNA testing was available. 

The justices ruled 5-4 that inmates cannot use a federal civil rights law to press for advanced DNA testing that was unavailable at the time of the crime. 

Forty-four states and the federal government have laws allowing post-conviction access to biological evidence for such testing, but that number does not include Alaska, where William Osborne was sentenced 15 years ago for a vicious attack on an Anchorage woman. 

"He has no constitutional right to obtain post-conviction access to the state's evidence for DNA testing," Chief Justice John Roberts wrote for the majority. He was supported by his conservative colleagues Justices Antonin Scalia, Anthony Kennedy, Clarence Thomas and Samuel Alito. 

In dissent, Justice John Paul Stevens said, "There is no reason to deny access to the evidence and there are many reasons to provide it, not the least of which is a fundamental concern in ensuring that justice has been done in this case." Justices David Souter, Ruth Bader Ginsburg and Stephen Breyer backed his conclusions. 

Osborne's trial attorney in Anchorage made a strategic decision 16 years ago to forgo more sophisticated DNA testing of the evidence in the criminal assault case, believing it might end up working against her client. Several years later, the Alaska inmate sought access to the state's biological evidence to have a state-of-the-art DNA test done. 
Where was someone in jail?
Alaska, where William Osborne was sentenced