"Tom, Dick or Harry" is a show tune from the Cole Porter musical, Kiss Me, Kate, introduced on Broadway on December 30, 1948 by Lisa Kirk (as Bianca); Harold Lang (as Lucentio); Edwin Clay (as Gremio); and Charles Wood (as Hortensio).
In the 1953 Hollywood film version, "Tom, Dick or Harry" was performed by Ann Miller (as Bianca), Tommy Rall (as Lucentio), Bobby Van (as Gremio), and Bob Fosse (as Hortensio).
Whereas other songs from Kiss Me, Kate (such as "So in Love" and "Too Darn Hot") were released as singles and achieved commercial success outside the show ("So in Love" reached the top ten on the Hit Parade in 1949 and has since been covered by scores of recording artists), "Tom, Dick or Harry" was written expressly to advance the Shrew subplot and is, therefore, a showtune in the truest sense of the word.
Perhaps the best-known example of this is Frank Sinatra's Kiss Me, Kate studio album which is part of his four-album (four-show) project that also includes Finian's Rainbow (1947), South Pacific (1949), and Guys and Dolls (1950), and which he produced in 1963 to promote his fledgling label, Reprise Records; hence the project title being the star-studded Reprise Musical Repertory Theatre.
[1] On May 18, 2000, "Tom, Dick or Harry" was performed on NBC-TV's Today show by 1999 Broadway revival cast members Amy Spanger (as Bianca), Michael Berresse (as Lucentio), Kevin Neal McCready (as Gremio), and Darren Lee (as Hortensio) as a result of the show having garnered the greatest number of Tony nominations (twelve) for that year.