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In Tuesday’s legal papers, Ms. Taylor and her colleagues said Mrs. Kane’s position was “not based on the holding of any court that has binding effect in Pennsylvania.”

Moreover, it said, the Supreme Court ruling that Mrs. Kane was relying on “in no way” says that a state law resembling Pennsylvania’s marriage law violates the Constitution.

James D. Schultz, general counsel for the governor, said in a letter Tuesday to her office that Mrs. Kane’s actions were “an improper usurpation” of the role of the courts, and her “personal opinion” was “not a valid basis for her refusal to do her job.”