The U.S. Supreme Court on Monday turned away a challenge to Utah’s anti-bigamy law brought by the polygamist stars of the popular reality television show “Sister Wives.”

The justices declined to take up an appeal by Kody Brown and his four wives, only one of whom he is legally married to, of a lower court’s ruling that threw out their challenge that claimed Utah’s law banning multiple spouses violated their religious liberty rights under the U.S. Constitution’s First Amendment.

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They also claimed the law violated their legally protected right to privacy.

After the show first aired on cable television network TLC in 2010, authorities in Utah announced they were investigating the family for violations of the anti-bigamy law. Fearing criminal prosecution, the family moved to Nevada in 2011.

The Utah law prohibits not only polygamy but also cohabitation by married people.

“Sister Wives” revolves around the lives of Kody Brown and wives Meri, Janelle, Christine and Robyn, as well as their many children. The family has a religious belief in polygamy, according to court papers.

Brown and the four women are fundamentalist Mormons, part of the Apostolic United Brethren Church.

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The family sued Utah authorities in Salt Lake City federal court. The district court found that part of the law relating to cohabitation violated the Constitution but the rest was lawful. The family appealed but the Denver-based 10th U.S. Circuit Court of Appeals tossed out the case because Kody Brown and the four women “faced no credible threat of prosecution.”

While Utah’s state attorney general had a policy not to prosecute polygamists under the anti-bigamy law unless other crimes were involved, such as child abuse or domestic violence, Jeffrey Buhman, the county attorney for Utah County, did not have a similar policy in place.

During the litigation, however, Buhman adopted the same prosecution policy, prompting the 10th Circuit to throw out the case.

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The family appealed to the Supreme Court. They should not be blocked from moving forward with their suit based on a new policy that could easily be revoked by officials in the future, the family told the justices.

The case in the Supreme Court of the United States is Kody Brown et al v. Jeffrey Buhman, No. 16-333.

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(Reporting by Andrew Chung; Editing by Will Dunham)