Prolific writer Anna Katharine Green was born in Brooklyn in 1846. In 1878 she published the novel The Leavenworth Case, which is generally regarded as the first detective story authored by a woman. The novel's title still sounds contemporary enough to be the next John Grisham legal thriller--indeed it was subtitled "A Lawyer's Story." The Leavenworth Case was a huge hit and Green became a bestselling author, publishing more than 40 books. Agatha Christie counted Green an influence.
Of course it's debatable what constitutes detective fiction: some believe the Old Testament story of Susanna and the Elders qualifies, which clearly predates Ms. Green! (Just the way Green predates Ms.)
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