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Kody Brown, centre, poses with his wives, from left, Janelle, Christine, Meri, and Robyn in a promotional photo for TLC's reality TV show, Sister Wives. (Bryant Livingston, Associated Press)

Kody Brown and his four wives want what any family wants, to live in the privacy of their own home free from government intrusion, and out from under the threat of criminal prosecution for — as they see it — just loving each other.

The polygamous family, stars of the U.S. television show Sister Wives, which airs on TLC, has sued Utah and the county they fled from, hoping to persuade a federal judge to overturn the state's bigamy law as unconstitutional.

The case could potentially decriminalize a way of life for tens of thousands of self-described Mormon fundamentalists, most of whom live in Utah where bigamy is a third-degree felony punishable by up to five years in prison.

The state, meanwhile, has publicly said it won't prosecute consenting adult polygamists unless there are other crimes involved, but insists the law doesn't overreach.

"It is not protected under religious freedom because states have the right to regulate marriage," said Paul Murphy, spokesman for Utah Attorney General Mark Shurtleff.

A hearing was set for Wednesday on a motion to dismiss the case after prosecutors in Utah County, where the family had been living until last year, announced no criminal charges would be filed against the Browns under the state's bigamy statute.

Utah County Attorney Jeff Buhman is seeking to have the lawsuit dismissed outright. He claims the Browns have no standing since they are no longer subject to prosecution.

No matter, claims their attorney, Washington, D.C., constitutional law professor Jonathan Turley.

Brown and his wives — Meri, Janelle, Christine and Robyn — remain victims and continue to live under the stigma of being considered felons, Turley said, noting they fled to Nevada last year.

While all states outlaw bigamy, some like Utah have laws that not only prohibit citizens from having more than one marriage license, but also make it illegal to even purport to be married to multiple partners. Utah's bigamy statute even bans unmarried adults from living together and having a sexual relationship.

The latter provision could include same-sex couples, unmarried heterosexual couples and those, like the Browns, who don't have multiple licenses but live in a marriage-like relationship.

Utah's statehood was granted in the 1890s under the condition that plural marriage — which was then openly practiced by members of The Church of Jesus Christ of Latter-day Saints — would be banned in the state constitution. The practice has been illegal under federal law in the U.S. since the 1860s.

The Browns say they practice polygamy as part of their religious beliefs. And like most polygamists, Brown only has a valid marriage license with his first wife. He married the other three in religious ceremonies. They consider themselves "spiritually married."