Complaint here:

http://jonathanturley.files.wordpress.com/2011/07/brown-complaint.pdf

<http://jonathanturley.files.wordpress.com/2011/07/brown-complaint.pdf>There's
a Free Exercise claim, but otherwise the complaint is rather vague on the
religious angle, focusing more on the "cohabitation" prong of the statute
(which as I noted is rarely if ever enforced).  Paragraph 191 states that
the plaintiffs "call each other spouses under their private religious
beliefs," and that "they would not be prosecuted if they claimed no
religious *obligation* and merely had casual or purely sexual
associations"-- the argument I've been pressing here-- but the complaint
does not otherwise explain the nature of the religious "obligation" or its
source.  Paragraph 117 merely states, without further elaboration, that the
three wives who are not civilly married to Kody Brown "considered themselves
committed to him as 'sister wives.'"  There's no mention of any religious
ceremony, for instance -- perhaps because the state would use that as
evidence of the crime, as in *Holm*.