Abstract: A horizontal functional Φ_H for the maps from Riemannian manifold to pseudo-Hermitian manifold was introduced, the critical maps of this functional were called CC-stationary maps. Then by using horizontal stress-energy tensor, some monotonicity formulas and Liouville type theorems were obtained for the horizontal CC-stationary maps from Riemannian manifold to pseudo-Hermitian manifold or the CC-stationary maps from Riemannian manifold to Sasakian manifold.