The lawsuit was filed on Thursday and released on a court website on Friday.
Religious organizations, individuals and corporations have filed scores of suits to block a planned mandate that employers generally include coverage of contraception in health insurance plans they offer workers.
Though the mandate has some exceptions for religious employers, the New York archdiocese, one of the largest in the United States, said it expected to incur nearly $200 million each year in penalties if it refuses to comply.
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