Rittman was born in Mannheim, Germany in 1908 and came to the United States in 1937. She worked as a concert accompanist and pianist for George Balanchine's American Ballet Caravan, then as a concert accompanist for Agnes de Mille, who invited her to arrange the dance music for the 1943 musical One Touch of Venus (which de Mille was choreographing). Thus began Rittman's lengthy Broadway career.
The many shows for which she created dance music arrangements include Carousel, Finian's Rainbow, Brigadoon, Allegro, Look, Ma, I'm Dancin'!, Miss Liberty, Gentlemen Prefer Blondes, The King and I, Paint Your Wagon, The Girl in Pink Tights, My Fair Lady, Christine, Camelot, On a Clear Day You Can See Forever, and Darling of the Day. Rittman also worked as a rehearsal pianist, musical assistant, and/or choral arranger on such other shows as Billion Dollar Baby, Brigadoon, South Pacific, both the Bernstein and the Leigh-Charlap-Styne-Comden-Green versions of Peter Pan, and The Sound of Music.
Rittman is survived by her nephew, Peter Krebs.