[2] While in Sydney, he taught at Whalan High School and developed his conducting skills with the University of NSW Choral Society and the Lachrymae Singers, which he founded.
In the early 1980s he became a conductor of the Flinders University Choral Society and Graduate Singers[4][6] and founded the small vocal ensemble Canticle.
[17] Crossin founded the Adelaide Chamber Singers in 1985,[18] and as director he has toured with them to Britain, Europe, North America and South-East Asia, won several awards for performance and CD recordings, and represented Australia in international choral and music education symposia and festivals.
4 "Star Chant" by Ross Edwards and Fred Watson with the Adelaide Chamber Singers under Crossin's direction won the prize for Vocal or Choral Work of the Year in the APRA Music Awards of 2008.
[20] In recent years, Crossin has turned to composition, mostly for voices, and his choral works have been performed not only by a number of Adelaide-based ensembles (Syntony, Adelaide Voices, Elder Conservatorium Chorale, Graduate Singers and Adelaide Chamber Singers) but by interstate and overseas choirs as well.