The same term is used here. Whether they are legal is determined by state law. Right now 23 states do not allow closed shops and 27 states do allow them.
http://en.wikipedia.org/wiki/Right_to_work_state#U.S._states_with_right-to-work_laws
The states marked in blue are where closed shops are illegal.
That’s appalling - is there no political effort to abolish such Marxist ‘principles’ in these states?