  Let $A$ be an abelian variety, and $G \subset Aut(A)$ a finite group acting
freely in codimension two. We discuss whether the singular quotient $A/G$
admits a resolution that is a Calabi-Yau manifold. While Oguiso constructed two
examples in dimension $3$, we show that there are none in dimension $4$. We
also classify up to isogeny the possible abelian varieties $A$ in arbitrary
dimension.
