  Conditions for spontaneous Charge-Parity (CP) violation in the scalar
potential sector of general $S(3)$ Higgs-doublet model (3HDM) are analyzed. An
analysis of the Higgs sector of the minimal $S(3)$-invariant extension of the
Standard Model including CP violation arising from the spontaneous breaking of
the electroweak symmetry is presented. This extended Higgs sector with three
SU(2) doublets Higgs fields with complex vev's provides an interesting scenario
to analyze the Higgs masses spectrum, trilinear self-couplings and CP
violation. We present how the spontaneous electroweak symmetry breaking, coming
from three $S(3)$ Higgs fields, gives an interesting scenario with nine
physical Higgs and three Goldstone bosons, when spontaneous CP violation arises
from the Higgs field $S(3)$ singlet $H_S$.
