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The non-Abelian gauge structure of the Standard Model implies the presence of the multi-boson self-interactions. Precise measurements in experimental and theoretical studies of these interactions allow not only testing the nature of the Standard Model but also new physics contribution coming from the beyond Standard Model. These interactions can be examined using a model-independent way in effective theory approach that composes the motivation part of this study. In this paper, we examine the anomalous $ZZγ$ and $Zγγ$ neutral triple gauge couplings via the process $e^{-} e^{+}\to Zγ$ for the neutrino-antineutrino pair decay of $Z$ boson. It has performed with both unpolarized and polarized electron beams at the Compact Linear Collider with $\sqrt{s}= 3$ TeV. The study focused on $CP$-conserving $C_{\widetilde{B}W}/{Λ^4}$ and $CP$-violating $C_{BB}/{Λ^4}$, $C_{BW}/{Λ^4}$, $C_{WW}/{Λ^4}$ couplings. Obtained sensitivities on the anomalous neutral triple gauge couplings with $95\%$ Confidence Level are given with systematic uncertainties of $0\%$, $5\%$ and $10\%$ for unpolarized, $-80\%$ and $80\%$ polarized electron beams with integrated luminosities of ${\cal L}_{\text{int}}=5$ $\rm ab^{-1}$, ${\cal L}_{\text{int}}=4$ $\rm ab^{-1}$ and ${\cal L}_{\text{int}}=1$ $\rm ab^{-1}$, respectively. Comparing the latest experimental limits and related phenomenological studies, our results on the anomalous neutral gauge couplings are set more stringent sensitivity between 10-30 times of magnitude.