She was born on February 4, 1900, in Vienna as Henrietta Rita Pollak. She took her first married name in 1921 upon wedding the Viennese physician Rudolf Kurzmann. From 1915 until her graduation, she studied piano at the Vienna Academy of Music.
From 1918 to 1923, she studied chemistry and physics at the University of Vienna, followed by musicology and additionally philosophy. She received her doctorate in musicology in 1924 under Professor Guido Adler, with a dissertation titled Die Modulation in den Instrumentalwerken Mozarts (Modulation in Mozart's Instrumental Works).
She began her career as a concert pianist in 1926, frequently performing at Vienna's Konzerthaus. A year later, she joined the faculty of the New Vienna Conservatory. In the early 1930s, she became secretary (board member) of the Austrian Section of the ISCM. From the 1930s onward, she produced radio programs for Austrian Radio (RAVAG) devoted to the works of many leading contemporary composers (Bartók, Berg, Krenek, Webern, and others). Her apartment often served as a venue for lecture series on new music, given by some of the aforementioned Austrian composers.
A noteworthy event in Kurzmann's career was her creation of a piano transcription of his Violin Concerto, which the composer discussed with her two months before his death. In 1936, together with her second husband Erwin Leuchter, a musicologist and conductor, she emigrated to Buenos Aires, where she died in 1942. In the Argentine capital, Kurzmann established herself successfully as a pianist, pedagogue, and editor of numerous publications on musical subjects. With the esteemed publishing house Ricordi Americana S.A. Buenos Aires, she published, among other works, an edition of Robert Schumann's songs.
In July 1931, Rita Kurzmann achieved a major pianistic success at a concert in Oxford as part of the ISCM Festival. At the Sheldonian Theatre, the artist performed the Sonatina for Piano, Op. 21 by Otton Jokl—a student of Alban Berg. On this occasion she met Józef Koffler, as she mentions in a letter to Jokl from October 1931, listing the Polish composer among those with whom she discussed the performed work.
Kurzmann and Koffler likely knew each other earlier from Vienna—both had studied musicology under Adler (Koffler received his doctorate in 1923). Moreover, Kurzmann gave concerts in Lviv, so it can be assumed that her performances in that city were connected to a personal acquaintance with the composer. It is also possible that Koffler's plans to emigrate to South America were inspired by Kurzmann's departure for Buenos Aires a year earlier.