  We analyze the neutralino-nucleus elastic cross-section in the MSSM,
including contributions from CP-violating phases, using the four-fermi
neutralino-quark interaction. Over a wide range of the MSSM parameter space we
show the variations in the cross-sections due to these phases. We further
concentrate on the regions which are consistent with constraints from the
electric dipole moment of the electron, neutron and mercury atom. In the
regions we examine in detail, we find suppressions by up to a factor of two,
while enhancements in the cross-sections are no greater than $\sim$ 10%.
