Nielsen, 71, was accused of marrying three women in 2006, two of them on the same day, the San Angelo Standard-Times reported. Each of the three counts of third-degree felony bigamy could earn Nielsen 2-10 years in prison and a $10,000 fine.
This was the first bigamy case to go to trial as a result of an April 2008 raid on the polygamist group's Yearning for Zion Ranch near Eldorado. Police searched the ranch after learning of possible sexual abuse.
Then-church leader Warren Jeffs -- who was arrested as part of the raid -- is serving life plus 20 years in prison for sexually assaulting a 12-year-old and a 15-year-old girl. He is scheduled for a bigamy trial, the newspaper said.
Court documents allege Nielsen married 34 women in addition to his legal wife, Linda Black, and presided over the marriage ceremonies of 12- and 16-year-old girls to Jeffs.
The fundamentalist group is not affiliated with mainstream Mormonism, which does not allow polygamy.