Does OSHA require hard hats to be worn with the bill facing forward?
ANSI only tests and certifies hard hats to be worn with the bill forward. Hard hats worn with the bill to the rear would not be considered reliable protection and would not meet the requirements. If the manufacturer certifies that it would be acceptable to wear the hard hat with the bill to the rear then you could wear it when the hard hat liner is turned, however you must get the approval of the manufacture.
