A polygamous family from TV's "Sister Wives" filed a request Monday for the U.S. Supreme Court to hear their case for legalizing polygamy.

Kody Brown and his four wives want the high court to review an appeal court's decision that upheld a unique provision of Utah's polygamy law that bans cohabitation with other partners even if the man is legally married to just one woman.

The ruling overturned a previous legal victory for the Browns in which a lower court ruled the law violated polygamists' right to privacy and religious freedom.

The appeals court decided in April that the Browns can't sue because they weren't charged under the Utah law. It didn't consider the constitutional issues.

Like most polygamous families, Brown is legally married to one wife and "spiritually married" to the others.

Utah prosecutors say they generally leave polygamists alone but need the ban to pursue polygamists for other crimes such as underage marriage and sexual assault.

The Browns took the case to the nation's highest court after the 10th U.S. Circuit Court of Appeals denied a request to reconsider it.

They face long odds. In recent years the U.S. Supreme Court has heard no more than 1 percent of the 7,500-plus cases appealed annually.

The family's attorney, Jonathan Turley, said in a statement the appeals court ruling curtailed the right for plural families to be heard in federal court.

"This has been an extended and difficult struggle for the Brown family but they have never wavered in their commitment to defending the important principles of religious freedom in this case," Turley said. "Utah is a state that was founded by courageous citizens seeking these very protections from government abuse and religious inequality. This lawsuit is true to the original dream of those seeking freedom in Utah."

The Utah Attorney General's Office declined comment on the petition.

The Browns, who now live in Las Vegas, say the Utah law has a chilling effect by sending law-abiding plural families into hiding because of fear of prosecution. The Browns say they fled their longtime home of Lehi, Utah, in 2011 because local authorities had opened an investigation.

The investigation was closed without filing charges, but the Browns say the threat of prosecution still exists. Turley argues that the investigation that began after the Brown's reality TV show "Sister Wives" premiered in 2010 amounted to government abuse.

There are an estimated 38,000 fundamentalist Mormons who practice or believe in polygamy, most living in Utah and other Western states. They believe polygamy brings exaltation in heaven.

The mainstream Mormon church, called The Church of Jesus Christ of Latter-day Saints, abandoned polygamy in 1890 and prohibits the practice for its 15 million members worldwide.