PHOENIX — When an unfamiliar car drives into the small neighboring towns of Colorado City, Ariz., and Hildale, Utah, private security agents working for the polygamist sect that dominates the towns ask the local marshals, who act as the police for both towns, to run the license plates to see who is passing through, federal prosecutors said.

Women wear ankle-length dresses. Children are taught to distrust strangers. Men think they need to have at least three wives to earn eternal salvation.

Most of the 10,000 people who live in these towns live by the rules of the cloistered world they inhabit and the dictates of a polygamous sect, the Fundamentalist Church of Jesus Christ of Latter-day Saints, whose prophet, Warren S. Jeffs, is serving a life sentence for the sexual assault of underage girls he said were his wives. And now, in Federal District Court here, 12 jurors will be asked to decide whether the two municipalities are run in a way that discriminates against outsiders, depriving them of their housing and civil rights.

According to the federal government’s complaint, originally filed in 2012, the towns and their utilities “have engaged in a pattern or practice of illegal discrimination against individuals who are not members of the Fundamentalist Church of Jesus Christ of Latter-day Saints.”