  In the present paper, we investigate some properties of the distributions
involved in the definition of a CR-statistical submanifold. The
characterization of a CR-product in holomorphic statistical manifolds is given.
By using an optimization technique, we establish a relationship between the
Ricci curvature and the squared norm of the mean curvature of any submanifold
in the same ambient space. The equality case is also discussed here. This paper
finishes with some related examples.
