The polygamous family from the popular cable TV show "Sister Wives" wants to change the Utah bigamy law that makes their plural marriage illegal.

A lawyer representing Kody Brown and his four wives said he will file a lawsuit against the state, Wednesday.

The family recently left Utah after police launched an investigation of their lifestyle.

Bigamy is a third-degree felony in Utah. A person can be found guilty of bigamy through cohabitation, not just legal marriage contracts.

The Browns' lawyer, Jonathan Turley, says the suit will challenge Utah's right to prosecute people for their private relationships.

In a statement released online Turley said, "We are not demanding the recognition of polygamous marriage."

"We are only challenging the right of the state to prosecute people for their private relations and demanding equal treatment with other citizens in living their lives according to their own beliefs," he explained.

Turley said he believes the case represents the "strongest factual and legal basis for a challenge to the criminalization of polygamy" ever filed in the federal courts.

Brown is only legally married to Meri Brown, but has three other wives -- Janelle, Christine and Robyn.  They have 16 children between them.