Abstract
Let $\bar{Y}$ be a normal surface that is the canonical $\mu_2$- or $\alpha_2$-covering of a classical or supersingular Enriques surface in characteristic 2. We determine all possible configurations of singularities on $\bar{Y}$, and for each configuration we describe which type of Enriques surfaces (classical or supersingular) appear as quotients of $\bar{Y}$.