The notion of $CR$-submanifolds of a Kaehler manifold was introduced by A. Bejancu [1]. Later, $CR$-submanifoIds of a Sasaki an manifold were studied by M. Kobayashi [7]. In this paper, we shall study some properties of a $D$-totally geodesic and $D^{\bot}$-totally geodesic $CR$-submanifold of a Sasakian manifold We also study the Ricci tensor and scalar curvature of $D$-minimal and $D^{\bot}$-minimal $CR$-submanifo1d of a Sasakian space form.