The court, without comment, rejected an appeal in which lawyers for Nichols said his federal conviction for conspiring to use weapons of mass destruction should be overturned because prosecutors failed to prove he intended to kill anyone.
The court acted in several other cases Tuesday, including three involving church and state issues.
The justices refused to let Pennsylvania include religious publications and items among the materials it exempts from sales taxes. Although the ruling sets no legal precedent, it does leave many other states with similar tax laws vulnerable to challenge.
The court refused to let state officials in New York resurrect a public school district for a community of Hasidic Jews. The court, by a 6-3 vote, turned away the state's argument that its third attempt to create a district for disabled children in the Kiryas Joel community does not breach the constitutionally required separation of church and state.
And the court let Maine subsidize children attending private, nonreligious schools while refusing to spend state money for those who go to religious schools.
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Ranching and farming groups won a hearing for their challenge to the Clinton administration's regulation of livestock grazing on millions of acres of federal and throughout the West. The court voted to study an appeal that says the administration's 1995 rules violate a 65-year-old law and threaten the livelihood of tens of thousands of ranchers.
Nichols, 44, was sentenced in 1997 to life in prison after he was found guilty in a federal trial of involuntary manslaughter and conspiracy for his role in the April 19, 1995, bombing of the Alfred P. Murrah Federal Building.
He was acquitted on federal charges of first- and second-degree murder.
Nichols faces another trial in an Oklahoma court on state murder charges. That trial is expected to begin late next year or in early 2001, and prosecutors are seeking the death penalty.
The Oklahoma Supreme Court last month approved nearly $1 million toward Nichols' defense in that trial.
Co-conspirator Timothy McVeigh, was sentenced to death for first-degree murder and other crimes in connection with the bombing after his federal conviction.
In the appeal acted on Tuesday, lawyers for Nichols said, "The government's evidence failed to prove that Mr. Nichols was aware that Mr. McVeigh intended to kill."
But Clinton administration lawyers urged the justices to reject the appeal, contending that Nichols' intent would be relevant only if he had been sentenced to death.
The federal law at issue allows the death penalty "if death results" from a conspiracy to use weapons of mass destruction. Nichols' lawyers said such language makes intent to kill an element of the crime, but government lawyers disagreed.
"A finding of resulting death raises the possibility of capital punishment," but does not impose any finding of murderous intent for the underlying crime, they said.
The 10th U.S. Circuit Court of Appeals agreed with that reasoning when it upheld Nichols' life sentence in February.