  We study possible deviations from the standard model in the reaction $\gamma
e\rightarrow Ze$ at a 500 GeV $e^+e^-$ collider. As a photon source we use a
laser backscattered photon beam. We investigate the most general $\gamma
Z\gamma$ and $\gamma ZZ$ vertices including operators up to
energy-dimension-six which are Lorentz invariant. These vertices require four
extra parameters; two are CP-conserving, $h^\gamma_1$ and $h^Z_1$, and two are
CP-violating, $h^\gamma_2$ and $h^Z_2$. We present analytical expressions of
the helicity amplitudes for the process $\gamma e\rightarrow Ze$ for arbitrary
values of anomalous couplings. Assuming Standard Model values are actually
measured we present the allowed region in the ($h^\gamma_1,h^Z_1$) plane at the
90\% confidence level. We then show how the angular correlation of the $Z$
decay products can be used to extract detailed information on the anomalous
(especially CP-violating) $\gamma Z\gamma$ and $\gamma ZZ$ couplings.
