We discuss the formulation of the general two-Higgs doublet model type III, which incorporates flavor changing neutral scalar interactions (FCNSI) and CP violation from several sources. CP violation can arise either from Yukawa terms or from the Higgs potential, be it explicit or spontaneous. We discuss the limit that includes CP violation and Yukawa four textures to control FCNSI and evaluate the CP asymmetry for the decay h → bcW, which may allow to test the patterns of FCNSI and CP violation, that arises in these models.