  We consider neutralino production and decay e^+e^ --> chi^0_i chi^0_j,
chi^0_j --> chi^0_1 f \bar{f} at a linear collider with transverse e^+ and e^-
beam polarization. We propose CP asymmetries by means of the azimuthal
distribution of the produced neutralinos and of that of the final leptons,
while taking also into account the subsequent decays of the neutralinos. We
include the complete spin correlations between production and decay. Our
framework is the Minimal Supersymmetric Standard Model with complex parameters.
In a numerical study we show that there are good prospects to observe these CP
asymmetries at the International Linear Collider and estimate the accuracy
expected for the determination of the phases in the neutralino sector.
