A lesbian couple from Westchester yesterday filed the first suit against a Catholic institution for refusing to recognize New York’s gay-marriage law.

The Manhattan federal court filing says the women — identified only as “Jane Roe” and “Jane Doe” — were wed Oct. 15, and that “Roe,” who’s worked at St. Joseph’s Medical Center in Yonkers since 2007, later applied to add “Doe” to her medical-benefits coverage.

But the request was denied by both St. Joseph’s and its insurance administrator, Empire Blue Cross Blue Shield, because hospital policy excludes same-sex spouses.

The class-action suit seeks an order declaring that both women are entitled to insurance coverage under federal law. It also says “thousands of legally married, same-sex couples” have been, or will be, denied benefits under similar policies administered by Empire, which is also named as a defendant.

The women are seeking an injunction ordering Blue Cross Blue Shield not to acquiesce to a company that wants to deny same-sex benefits because of religious beliefs, said Jeffrey Norton, their lawyer.

Empire declined to comment. St. Joseph’s didn’t return messages.