Nichols has already been convicted on federal charges for his role in the 1995 bombing that killed 168 people. At issue now is the state's effort to try him on more charges.
Justices, without comment, turned back his claims that another trial would be double jeopardy.
The refusal is the latest in a string of Supreme Court losses for Nichols, who was convicted of conspiracy and involuntary manslaughter in the attack on the Oklahoma City federal office building. Timothy McVeigh, the bombing's mastermind, was executed in June.
Justices refused in October to consider arguments that the FBI's belated release of investigation documents to Nichols' attorneys affected his federal trial. And last spring Nichols lost an appeal of his conviction.
Those cases pit Nichols against the federal government, which won convictions but not the death penalty. The latest case involves the state's plans to try him on 160 counts of first-degree murder among other charges.
Nichols' lawyer, Brian Hermanson, said federal and state officers and prosecutors worked together on the investigation and 1997 trial that ended with Nichols' federal sentence of life in prison.
"The power and majesty of the federal sovereign and a state sovereign were conjoined in a massive criminal law enforcement enterprise which at first worked jointly to convict Mr. Nichols, and now seeks to separate one from the other to try him again for the same offenses," Hermanson wrote.
Oklahoma prosecutors said they planned all along to follow the federal trial regardless of the outcome with a state trial.
"Although (Nichols) alleges that this was a 'massive, well-funded and sophisticated joint federal-state law enforcement enterprise,' they have failed to prove that it was a joint enterprise in any form or fashion," Oklahoma prosecutor John Jacobsen wrote in the government's case.
The April 19, 1995, bombing of the Alfred P. Murrah Federal Building, which killed 168 and injured more than 500, was at the time the worst act of terrorism on U.S. soil.
Hermanson said the government charges are similar to ones of which Nichols was acquitted by a federal jury.
"This opens the door a little more for a state trial for Nichols but there still are some obstacles," said CBS News legal analyst Andrew Cohen. "Legally, Nichols still has an appeal or two alive in the federal courts, which might delay any state trial."
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