A smooth manifold is called a statistical manifold if it is endowed with a torsion-free affine connection \(\nabla\) and a Riemannian metric \(h\) so that the 3-form \(\nabla h\) is symmetric. This paper is devoted to the conformal-projective geometry of statistical manifolds, a natural generalization of the conformal geometry of Riemannian manifolds. It is found a criterion for two statistical manifolds to be conformally-projectively equivalent. The conformal-projective curvature tensor is introduced. It is shown that a statistical manifold is conformally-projectively flat iff its conformal-projective curvature tensor is zero. It is proved that a conformally-projectively flat statistical manifold can be embedded into a suitable flat statistical manifold as a statistical submanifold of codimension two.