  The first-order bosonic string theory, perturbed by primary operator,
corresponding to the deformation of target-space complex structure is
considered. We compute the correlation functions in this theory and study their
divergencies. It is found, that consistency of these correlation functions with
the world-sheet conformal invariance requires the Kodaira-Spencer equations to
be satisfied by target-space Beltrami differentials. This statement is checked
explicitly for the three-point and four-point correlators, containing one probe
operator. We discuss the origin of these divergences and their relation with
beta-functions or effective action and polyvertex structures in BRST approach.
