nLab
model structure on crossed complexes

Brown and Golasinski gave a model category structure on the category of crossed complexs in

• Ronald Brown and Marek Golasinski, A model structure for the homotopy theory of crossed complexes, Cahiers de Topologie et Géométrie Différentielle Catégoriques, 30 no. 1 (1989), p. 61-82 (pdf)

Notice that by Brown-Higgins, crossed complexes are equivalent to strict omega-groupoids.