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A polygamous family made famous by a reality TV show can't challenge Utah's law banning polygamy because they probably won't be prosecuted under it, according to state attorneys who want the "Sister Wives" lawsuit dismissed.

"It is no secret that polygamists live in Utah County," attorneys argued in a motion to dismiss filed Friday. "Yet no one has any memory of when the last prosecution for polygamy occurred in Utah County."

Former Lehi residents Kody Brown and his four wives, who star in the TLC reality show "Sister Wives," filed a federal lawsuit in July seeking to strike down Utah's bigamy law. The suit rests primarily on the right to privacy in intimate relationships — a legal principle also at the heart of the gay-rights movement.

But Utah Attorney General Mark Shurtleff's policy has been to leave the state's approximately 30,000 polygamists alone unless they marry underage girls or engage in some other kind of abuse, according to the motion to dismiss.

Since 1960, only three criminal bigamy cases have been appealed in Utah, and they were all in conjunction with another crime, state attorneys wrote.

Since the Browns do not appear to have committed any other crimes, "it is unlikely they will face prosecution under the bigamy statute," the motion states. It was filed by attorneys for Shurtleff, Gov. Gary Herbert and Utah County Attorney Jeffrey Buhman.

Represented by a Washington, D.C.,-based constitutional law attorney, the Browns argue they have legal standing to challenge the state's bigamy law because they were investigated by the Lehi Police Department after their show debuted. That threat of prosecution, they said, forced them to move to Nevada and keeps them from freely visiting Utah.

But no charges have been filed against the Browns, even though Lehi police submitted their report to Buhman nearly a year ago, state attorneys wrote.

"Simply stated, there is a lack of history of prosecution of polygamy in Utah since the 1950s except when it is in conjunction with some other crime," the motion states.

The Browns' case, however, remains open, the Utah County Attorney's Office confirmed Tuesday. And the family says they are "denounced as presumptive felons by prosecutors in the media," according to their attorney, Jonathan Turley.

Calling the bigamy law, "unconstitutional," Turley said they will "vigorously oppose the effort to close the door of the courthouse to this family."

The lack of imminent threat of prosecution defeated the last attempt to overturn Utah's bigamy law four years ago, after a woman sued when she was denied a marriage license to become a man's second wife.

But the "Sister Wives" family is not seeking to have their marriages legally recognized, Turley said. Instead, they want polygamy to no longer be a felony.

The state's Friday motion to dismiss also invokes gay marriage, pointing to a 2009 suit filed by a lesbian couple challenging Oklahoma's law defining marriage as between a man and a woman. The courts there found the "alleged injury" couldn't be legally pinned to a single state official, and it was dismissed.

U.S. District Judge Clark Waddoups has not yet ruled on the motion. No hearings have been scheduled in the case — though three sealed summons have been served, according to court records.

Of the three other bigamy cases heard by Utah appellate courts, one from 1988 also involved fraud, and a second, against Juab County polygamist Tom Green, also involved nonsupport of spouses and children, according to the motion to dismiss.

A third case, against police officer Rodney Holm, also involved sex with a minor. The 2006 case of the Fundamentalist Church of Jesus Christ of Latter-Day Saints man convicted of having sex with a 16-year-old plural wife has come closest to being considered by the U.S. Supreme Court, which requested briefs in the case but did not end up hearing it.

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Full statement from 'Sister Wives' family attorney Jonathan Turley:

"This motion is an effort to avoid scrutiny of a state law that is facially unconstitutional. Under this extreme position, state officials can criminalize any private relationship while denying the right of citizens to challenge the law, even when those citizens are denounced as presumptive felons by prosecutors in the media. We will vigorously oppose the effort to close the door of the courthouse to this family."