A U.S. federal appeals court has upheld Utah's ban on polygamous cohabitation, inflicting defeat to a family featured on the reality show "Sister Wives." The family earlier asked the court to uphold a 2013 ruling in their favour.

The U.S. Court of Appeals for the Tenth Circuit ruled on Monday that the challenge to Utah's bigamy statute is "moot."

"It is not a 'Case' or 'Controversy' under Article III of the U.S. Constitution. We remand to the district court with instructions to vacate the judgment and dismiss this action," the appeals court ruled.

Under the Utah law, "a person is guilty of bigamy when, knowing he has a husband or wife or knowing the other person has a husband or wife, the person purports to marry another person or cohabits with another person."

Plaintiffs Kody Brown, Meri Brown, Janelle Brown, Christine Brown, and Robyn Sullivan form a "plural family." Kody Brown is legally married to Meri Brown and "spiritually married" to the other three women, whom he calls "sister wives."

When the Browns were featured in the TLC reality TV show in 2010, the Lehi Police Department opened an investigation of the Browns for violating a state law.

The family filed a case before a federal district court against the Utah governor and attorney general, saying the law violated their First and Fourteenth Amendment rights.

Judge Clark Waddoups ruled in December 2013 in favour of the Browns and the state appealed the case to the court of appeals.

Back then, Brown said "Sister Wives" became a venue to normalise polygamy before the public, the Christian News Network reports.

"When I talked with my children about doing the show, I said we have an opportunity to not only change our world, but to change the world for everyone else," he said.

The court then ruled that it "believes that Plaintiffs are correct in their argument that, in prohibiting cohabitation under the statute, 'it is, of course, the state that has equated private sexual conduct with marriage.'"

The Utah County Attorney's Office adopted a policy that it will bring bigamy prosecutions only against those who induce partner to marry through misrepresentation or are suspected of committing crime such as fraud or abuse.

However, the federal court denied the county attorney's motion to dismiss the case and granted a summary judgement to the Browns.

The appeals court ruled that the district court made an error by proceeding to the merits of the case.

"Federal courts are courts of limited jurisdiction. They lack power to decide issues—however important or fiercely contested—that are detached from a live dispute between the parties," the court ruled.

It said the case should have been dismissed since the Browns were never charged with a crime.

"The record shows the [prosecutor's office] has adopted, and intends to abide by, a policy under which the Browns face no threat of prosecution," wrote Judge Scott Matheson.

Brown said he plans to appeal the decision, either back to the 10th Circuit en banc or to the United States Supreme Court.