This is not true in any US state per the 1st amendment of the Constitution. What you may be thinking of are so-called "right to work" states which have effectively defanged unions by making it illegal to require union membership or payment of union dues as a condition of employment. (It's actually a little more complicated than that, but you can easily look it up if you want the details.)

Anyhow, the end result is that in "right to work" states it's almost impossible to unionize.