  In this paper, we consider some generalized holomorphic maps between
pseudo-Hermitian manifolds and Hermitian manifolds. By Bochner formulas and
comparison theorems, we establish related Schwarz type results. As corollaries,
Liouville theorem and little Picard theorem for basic CR functions are deduced.
Finally, we study CR Carath\'eodory pseudodistance on CR manifolds.
