  We study neutralino production at the linear collider with the subsequent
two-body decays ~chi^0_i -> ~chi^0_n Z^0 and Z^0 -> l^+ l^-, with l=e, mu, tau,
or Z^0 -> q q- with q=c,b. We show that transverse electron and positron beam
polarizations allow the definition of unique CP observables. These are
azimuthal asymmetries in the distributions of the final leptons or quarks. We
calculate these CP asymmetries and the cross sections in the Minimal
Supersymmetric Standard Model with complex higgsino and gaugino parameters mu
and M_1. For final quark pairs, we find CP asymmetries as large as 30%. We
discuss the significances for observing the CP asymmetries at the International
Linear Collider (ILC). Finally we compare the CP asymmetries with those
asymmetries which require unpolarized and/or longitudinally polarized beams
only.
