SALT LAKE CITY — A polygamous family made famous by a reality TV show won’t face charges if a Utah law banning plural marriage stays on the books, according to court documents filed Wednesday by prosecutors.

The state has a long-standing policy against prosecuting consenting adult polygamists. Still, prosecutors have argued the law should stand because it helps authorities go after those who commit domestic abuses.

The stars of the TV show “Sister Wives” previously filed a lawsuit challenging the law on constitutional grounds. However, the Utah attorney general says family members can’t challenge the statute because they’ve never been prosecuted under it.

Authorities knew about Kody Brown and his four wives long before they first appeared on TV in 2010. Questions from viewers of the show on the issue prompted a brief investigation, but the county attorney closed it without filing charges, prosecutors said.

The Browns contend that even though charges weren’t filed, they were labeled criminals and the fear of prosecution drove them from Utah to Nevada.

A lower court judge in Utah agreed that the threat of prosecution had a chilling effect on their freedom of speech and let the suit go forward. In 2013, U.S. District Judge Clark Waddoups found a key part of Utah’s bigamy law violates the Brown’s right to religious freedom and struck it down.

The state appealed his decision, and the 10th Circuit Court of Appeals is set to hear arguments in the case on Jan. 21.

Both sides filed new documents in the case Wednesday after the appeals court asked to hear more about whether the Browns have legal standing to challenge the law.

There are about 30,000 polygamists in Utah, prosecutors said. They believe polygamy brings exaltation in heaven – a legacy of the early Mormon church. The mainstream Salt Lake City-based Church of Jesus Christ of Latter-day Saints abandoned the practice in 1890 and strictly prohibits it today.

Utah has pointed to jailed polygamous leader Warren Jeffs as evidence that the practice can be associated with crimes such as sexual assault, statutory rape and exploitation of government benefits. They say outlawing it helps investigators gather evidence and strengthens cases against abusers.

The Brown family counters that polygamous unions can be healthy, and there are other laws to prosecute crimes that occur in polygamous and monogamous families.

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