  We consider an explicitly CP-violating model with two Higgs doublets and one
complex singlet scalar. The singlet $S$ is charged under a global $\rm U(1)$
symmetry which is softly broken by a mass term $\mu^2 S^2+\hc$. Imaginary part
of $S$ is a stable dark matter candidate which at the tree level, in the limit
of zero momentum transfer, decouples from nucleons naturally satisfying all
existing direct detection limits on dark matter scattering cross-section. It is
explicitly shown that within this framework in the alignment limit CP-violation
is still present in contrast to a popular version of a 2-Higgs doublet model
with softly broken $Z_2$ symmetry. In this context, we investigate dark matter
implications of the model both with and without CP violation in the scalar
sector. In particular, dark matter relic abundance is calculated and the
possibility for its indirect detection is discussed.
