Who really sang the female lead in the King and I?

In the original Broadway production of "The King and I," the female lead, Anna Leonowens, was played by Gertrude Lawrence, who performed the role and its songs. However, in the 1956 film adaptation, the character was portrayed by Deborah Kerr, who lip-synced to the singing voice of actress Marni Nixon. Nixon is well-known for providing the singing voice for several actresses in classic films.