Perelman wrote at least five original plays produced on Broadway from 1932 to 1963, two as collaborators with his wife Laura. The first was the musical revue "Walk a Little Faster", which opened in December 1932. With Ogden Nash, he wrote the book for the musical "One Touch of Venus" (music by Kurt Weill, lyrics by Nash), which opened on Broadway in 1943 and ran for more than 500 performances. His final play "The Beauty Part" (1962), which starred Bert Lahr in multiple roles, fared less well, its short run attributed in part to the 114-day 1962 New York City newspaper strike.