SALT LAKE CITY (July 25, 2012)--) - Kody Brown and his four wives, the polygamous stars of the TLC show "Sister Wives," are suing Utah and the county from which they fled, hoping to persuade a federal judge to overturn the state's bigamy law as unconstitutional.

The judge heard arguments Wednesday on a motion to dismiss the case.

He will rule later.

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

While the state has said it won't prosecute consenting adult polygamists unless there are other crimes involved, authorities insist the law doesn't overreach.