Norman's success with Getting Out led her to move to New York City where she continued to write for the Actors Theatre of Louisville.

The play brought Norman a great deal of recognition, dealing frankly with the subject of suicide, and won the 1983 Pulitzer Prize for Drama,[7] the Susan Smith Blackburn Prize,[8] the Hull-Warriner, the Drama Desk Award, and the 1986 Golden Plate Award of the American Academy of Achievement.

[9] However, her follow-up play, Traveller in the Dark received scathing reviews from the New York critics, some of whom were as blunt to say she could not have written it.

According to an interview in The New York Times, "Ms. Norman stayed away from the theater and turned to screenplays, including a 1986 movie adaptation of 'night, Mother that starred Sissy Spacek and Anne Bancroft and failed to impress critics.

[12] Norman and composer Jason Robert Brown made a symphonic adaptation of the children's novel The Trumpet of the Swan, which premiered at the Kennedy Center in 2008.

[13] Norman has since written the libretto for the musical adaptation of the film The Bridges of Madison County, with a score by Brown.

She has written the television films Face of a Stranger (1991),[15] A Cooler Climate (1999),[16] Custody of the Heart (2000),[17] and The Audrey Hepburn Story (2000).