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Utah Gov. Gary Richard Herbert, a Republican, said the 91-page decision is being reviewed and that he always is concerned when courts change public policy.

The Utah law, written in 1973, says that 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.”

Judge Waddoups ruled that the words “or cohabits with another person” violated the Browns’ constitutional rights under the free-exercise clause of the First Amendment and did not have a rational basis under the due process clause of the 14th Amendment. The ruling thus decriminalized “religious cohabitation” — a term preferred by Judge Waddoups — while keeping the law’s prohibition of having more than one legal spouse.

Mr. Brown and his polygamous family are members of the Apostolic United Brethren, a religion derived in the 19th century when Mormons practiced polygamy.

The Church of Jesus Christ of Latter-day Saints issued a statement repeating that its members do not practice polygamy and that Mormons have no affiliation with the AUB.

Mr. Brown lives with Meri Brown, Janelle Brown, Christine Brown, Robyn Sullvan and their 17 children, but is legally married only to Meri Brown. They do not seek multiple marriage licenses.

The Browns, represented by Washington lawyer Jonathan Turley and others, sued Utah County Attorney Jeffrey Buhman in 2011, saying the family was investigated after the first episode of “Sister Wives” aired on TLC Network.

In its defense, the state agreed that it denounced the Brown family but did not prosecute them. Mr. Buhman later said he would not prosecute the Browns unless he found that they “also committed a collateral crime.”

The Browns sued for relief from the law. Mr. Turley said he would be honored to defend the family in the 10th U.S. Circuit Court of Appeals and even to the Supreme Court, if necessary.

State Sen. Lyle Hillyard told The Washington Times this week that he did not know what Utah lawmakers will do about the ruling when they return in January.

One option is “not do anything,” Mr. Hillyard said, noting that lawmakers have not repealed other laws that are unenforced.

However, the Brown ruling is interesting because when Utah became a state in 1896, “one of the conditions Congress required in our Constitution is the forbidding of polygamy,” Mr. Hillyard said.

“Can a [federal] court now say, ‘Well, it’s part of your Constitution, and it’s a condition upon which you were adopted into statehood; now we’re going to say that’s no longer valid?’” he asked.