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As of this moment, 22 states and the District of Columbia have in place right to work statutes--a subset of union law that preserves the choice of workers to decide whether or not they wish to join a union that exists at their place of employment.
Because right to work law specifically deal with collective bargaining agreements and employer treatment of non-union employees, it's especially important for you to understand how they function and may limit your actions.
As you may already know, federal law protects the rights of employees who wish to unionize and engage in collective behavior. Congress, however, has generally left it up to the states to legislate union law when employees do not wish to be part of the organization.
Under section 14(b) of the Taft-Hartley Act, states may prohibit an agreement between a union and an employer that:
Statutes that have outlawed one or both of these are known as right to work laws.
If your business is in a right to work jurisdiction, this means that you cannot predicate employment on union membership, nor can you force employees to pay union fees. Employees can come and go from the union as they please without repercussion.
Keep in mind that union law and right to work statutes vary from state to state, with different punishments and exceptions. If you have any questions about what you can and cannot do, it's best to contact a local labor attorney for answers.