The paper deals with ``statistical manifolds'', i.e., with triples \((N, \nabla,h)\), where \(N\) is a manifold, \(\nabla\) is a torsion free affine connection and \(h\) is a pseudo-Riemannian metric such that \(\nabla h\) is symmetric. The authors prove several results concerning conformally flat statistical submanifolds and flat statistical manifolds.