  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 $ZZ\gamma$ and $Z\gamma\gamma$
neutral triple gauge couplings via the process $e^{-} e^{+}\to Z\gamma$ 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
$C_{\widetilde{B}W}/{\Lambda^4}$ and $CP$-violating $C_{BB}/{\Lambda^4}$,
$C_{BW}/{\Lambda^4}$, $C_{WW}/{\Lambda^4}$ 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.
