  We re-investigate the neutralino-nucleus elastic scattering as a promising
dark matter detection mechanism including contributions from the
scalar-pseudoscalar mixing of neutral Higgs states and the induced phase
between two Higgs doublets due to the CP-violating phases of the scalar top and
bottom sectors in the minimal supersymmetric standard model. The spin-dependent
part of the cross section turns out to be hardly affected by the CP-violating
induced phase due to a mutually destructive unavoidable suppression mechanism
of various relevant supersymmetric parameters. On the other hand, although the
phase $\Phi_\mu$ of the higgsino mass parameter is set to be zero, the
spin-independent part, which can dominate over the spin-dependent part for
heavy nuclei, can be strongly dependent on the CP-violating scalar-pseudoscalar
mixing and the induced phase, in particular, for a large $|\mu|$, a small
charged Higgs boson mass, and a large trilinear term $|A|$ compared to the SUSY
breaking scale. For a small $\tan\beta$ and a large $|\mu|$, the
spin-independent cross section is enhanced by an order of magnitude as the
phase $\Phi_A$ of the trilinear term increases up to $\pi$, while for a large
$\tan\beta$ and a large $|\mu|$ the spin-independent cross section is
significantly suppressed for non-zero values of the phase $\Phi_A$.
