  Once supersymmetric neutralinos $\tilde{\chi}^0$ are produced copiously at
$e^+e^-$ linear colliders, their characteristics can be measured with high
precision. In particular, the fundamental parameters in the gaugino/higgsino
sector of the minimal supersymmetric extension of the standard model (MSSM) can
be analyzed. Here we focus on the determination of possible CP--odd phases of
these parameters. To that end, we exploit the electron/positron beam
polarization, including transverse polarization, as well as the spin/angular
correlations of the neutralino production $e^+ e^- \to \tilde{\chi}^0_i
\tilde{\chi}^0_j$ and subsequent 2--body decays $\tilde{\chi}^0_i \to
\tilde{\chi}^0_k h, \tilde{\chi}^0_k Z, \tilde \ell^\pm_R \ell^\mp$, using
(partly) optimized CP--odd observables. If no final--state polarizations are
measured, the $Z$ and $h$ modes are independent of the $\tilde{\chi}^0_i$
polarization, but CP--odd observables constructed from the leptonic decay mode
can help in reconstructing the neutralino sector of the CP--noninvariant MSSM.
In this situation, transverse beam polarization does not seem to be
particularly useful in probing explicit CP violation in the neutralino sector
of the MSSM. This can most easily be accomplished using longitudinal beam
polarization.
