  We prove that metric measure spaces obtained as limits of closed Riemannian
manifolds with Ricci curvature satisfying a uniform Kato bound are rectifiable.
In the case of a non-collapsing assumption and a strong Kato bound, we
additionally show that for any $\alpha \in (0,1)$ the regular part of the space
lies in an open set with the structure of a $\mathcal{C}^\alpha$-manifold.
