Arguments are scheduled to start before the 7th Circuit Court of Appeals in Chicago on Monday.
In March, U.S. District Judge William Conley overturned a part of the law requiring that unions hold elections each year for members to retain their official status. The judge also said the law illegally halted automatic withdrawal of union dues. The majority of the law remained untouched.
The lawsuit is one of three pending in state or federal courts. A state court Sept. 14 threw out major parts of the 2011 law. The state is also appealing that ruling.