We study completely $\pi$-regular semigroups admitting a decomposition into a semilattice of $\sigma_n$-simple semigroups, and describe them in terms of properties of their idempotents. In the general case, semigroups admitting a decomposition into a semilattice of $\sigma_n$-simple semigroups were characterized by M. Ćirić and S. Bogdanović in [3] (see Theorem 1 below), in terms of paths of length $n$ in the graph corresponding to the relation $\longrightarrow$, and in terms of principal filters and $n$-radicals. Here we prove that in the completely $\pi$-regular case, it suffices to consider only those paths of length $n$ starting and/or ending with and idempotent, as well as principal filters and $n$-radicals generated by idempotents.