  In the minimal supersymmetric standard model (MSSM), the neutralinos, the
spin--1/2 Majorana superpartners of the neutral gauge and Higgs bosons, are
expected to be among the light supersymmetric particles that can be produced
copiously at future high--energy colliders. We analyze two--body neutralino
decays into a neutralino plus a $Z$ boson or a lightest neutral Higgs boson
$h$, allowing the relevant parameters to have complex phases. We show that the
two--body tree--level decays of neutralinos are kinematically allowed in a
large region of the MSSM parameter space and they can provide us with a
powerful probe of the Majorana nature and CP properties of the neutralinos
through the $Z$--boson polarization measured from $Z$--boson leptonic decays.
