  We show that if the universal cover of a closed smooth manifold admitting a
metric with non-negative Ricci curvature is formal, then the manifold itself is
formal. We reprove a result of Fiorenza-Kawai-L\^e-Schwachh\"ofer, that closed
orientable manifolds with a non-negative Ricci curvature metric and
sufficiently large first Betti number are formal. Our method allows us to
remove the orientability hypothesis; we further address some cases of
non-closed manifolds.
