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The Brown family, of the TLC show "Sister Wives," wants a rehearing in their case against the state of Utah.

On Monday, Kody Brown and his four wives — Meri, Janelle, Christine and Robyn — filed a petition for a rehearing in the 10th Circuit Court of Appeals. Earlier this month, a federal appeals court dismissed a landmark decision that decriminalized polygamy in Utah — a legal defeat for the Browns.

Formerly of Lehi, the family, which practices polygamy for religious reasons, moved to Nevada to avoid prosecution after the Utah County attorney's office and Lehi police investigated them for alleged bigamy, a felony punishable by up to five years in prison. The Browns filed a lawsuit against the Utah County attorney's office and the state.

But according to the appeals court, the Browns cannot sue the state over its ban on plural marriages because the family never faced charges, and local prosecutors later said they would not prosecute consenting adults with multiple wives.

The panel's decision reversed a 2013 ruling that removed the threat of arrest for polygamous families. U.S. District Judge Clark Waddoups had found that the possibility of prosecution drove the Browns out of the state and that key parts of Utah's bigamy law violated their right to privacy and religious freedom.

In 2013, Waddoups ruled in the Browns' favor. Waddoups let stand the portion of the statute that dealt with multiple marriage licenses.

Under Utah law, people are guilty of third-degree felony bigamy if they hold multiple marriage licenses or if, when already married, they cohabit with another consenting adult in a marriagelike relationship.

Twitter: @MikeyPanda

The Associated Press contributed to this story.