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Greenwood was the original choice to play "Aunt Eller" in the Broadway musical "Oklahoma!" In fact, the part was conceived with her in mind. Film commitments, however, kept her from doing the role and the part went to actress Betty Garde. As a testament to her popularity, Greenwood was asked to do the film version over a decade later.

Even when well into middle age, she could perform complete leg-splits as well as kick higher than the top of her own head - sideways!

Although she died in 1978, her death was not reported to the public until Valentines Day 1979 when an obituary appeared in the New York Times, stating she had no known survivors and that she left her personal papers to playwright William Luce as per her final wishes.

Originally had a prominent part in the Broadway version of "Annie Get Your Gun". At the insistence of star Ethel Merman, the part was pared down to almost nothing. When a dispirited Greenwood gave co-producer Richard Rodgers notice, a sympathetic Rodgers replied, "Letty, I can hardly blame you.".

Her first marriage to actor Cyril Ring, brother of screen legend Blanche Ring, ended in scandal after only six years; her second marriage to musician Martin Broones was long and happy.