In the present paper, we study Casorati curvatures for statistical hypersurfaces. We show that the normalized scalar curvature for any real hypersurface (i.e., statistical hypersurface) of a holomorphic statistical manifold of constant holomorphic sectional curvature $k$ is bounded above by the generalized normalized $\delta-$Casorati curvatures and also consider the equality case of the inequality. Some immediate applications are discussed.