Arizona Gov. Jan Brewer (R) signed the ban into law in April 2012, and nine other states have similar bans.
The Supreme Court justice showed up for jury duty Wednesday in D.C. Superior Court.
It is the second time the court has opted against hearing such a challenge.
Groups including the oil and chemical industry had challenged several aspects of the EPA's regulatory authority.
Napolitano is leaving the Department of Homeland Security to become president of the University of California.
The decisions are set to come down shortly after 10 a.m. eastern time. Stay tuned below for all the latest news, reaction and analysis.
Today, the Supreme Court effectively struck down part of the Voting Rights Act.
We didn't get the big decisions, but that doesn't mean there wasn't any news. Here's what you should know.
Thomas argued that he sides against the University of Texas's Affirmative Action policies, comparing the school's justifications to those of Jim Crow-era segregationists.
The Cross-State Air Pollution Rule would have reduced pollutants from coal-fired power plants.