  Complex Hantzsche-Wendt manifolds are flat K\"ahler manifolds with holonomy
group $\mathbb{Z}_2^{n-1}\subset SU(n)$. They are important example of
Calabi-Yau manifolds of abelian type. In this paper we describe them as
quotients of a product of elliptic curves by a finite group $\tilde{G}$. This
will allow us to classify all possible integral holonomy representations and
give an algorithm classifying their diffeomorphism types.
