  We investigate the effects of anomalous neutral triple gauge couplings in
$ZZ$ and $Z\gamma$ production processes, followed by the leptonic decay of the
$Z$ boson, at a lepton collider with center-of-mass energy $\sqrt{s}=250$~GeV
and polarized beams. We use an effective Lagrangian formalism to parameterize
the anomalous couplings in terms of dimension-8 operators $c_{\widetilde{B}W}$,
$c_{BW}$, $c_{WW}$, and $c_{BB}$, and study the sensitivity of observables such
as cross~section, polarization, and spin correlation as functions of these
couplings. We perform a Bayesian statistical analysis using Markov Chain Monte
Carlo methods to determine simultaneous limits on the anomalous couplings,
taking into account various luminosities $\mathcal{L} \in \{0.1~\text{ab}^{-1},
0.3~\text{ab}^{-1}, 1~\text{ab}^{-1}, 3~\text{ab}^{-1}, 10~\text{ab}^{-1}\}$
and systematic uncertainties. We find that polarization and spin correlation
observables significantly enhance the sensitivity to anomalous couplings,
providing stringent constraints on these couplings.
