The bigger question for many is how she is financing these activities. Liberty Central reported the initial $550,000 on its 2009 tax return, though the identities of the two donors are redacted.

A federal law requires justices to recuse themselves in a number of circumstances where real or perceived conflicts of interest could arise, including in cases where their spouses could have a financial interest. But the decision to step aside is up to each justice; there is no appeal from the nation’s highest court.

“It’s shocking that you would have a Supreme Court justice sitting on a case that might implicate in a very fundamental way the interests of someone who might have contributed to his wife’s organization,” said Deborah L. Rhode, a law professor and director of the Stanford University Center on the Legal Profession.

“The fact that we can’t find that out is the first problem,” she said, adding, “And how can the public form a judgment about propriety if it doesn’t have the basic underlying facts?”