Key points are not available for this paper at this time.
M. S. Baouendi, F. Treves, A Property of the Functions and Distributions Annihilated by a Locally Integrable System of Complex Vector Fields, Annals of Mathematics, Second Series, Vol. 113, No. 2 (Mar., 1981), pp. 387-421
Baouendi et al. (Sun,) studied this question.