The House had defeated the proposal recently but the Senate created a new version Thursday.
However, the House upheld Speaker Andy Tobin’s ruling that the new version violates a rule against combining unrelated legislation.
Attorney General Tom Horne had championed the bill.
He said Colorado City officers who are members of the Fundamentalist Church of Jesus Christ of Latter Day Saints flout the law and are simply replaced by other followers of imprisoned FLDS leader Warren Jeffs if removed individually.
Critics say the bill unfairly targets Colorado City and that current officers haven’t done anything wrong.