  In the quasielastic region, we investigate the effect of neutrino
electromagnetic properties constrained from the recent experiments on the
electroweak neutral current reaction process of the neutrino-$^{12}$C
scattering. For a relativistic description of the nuclear dynamics, we employ
the relativistic mean-field model, which has been proven to describe the data
nicely in the quasielastic region. In the present work, we analyze the
influence beyond the Standard Model by considering the neutrino magnetic and
electric dipole form factors and charge radius on the neutrino electroweak
interactions within $^{12}$C. To this end, we use the values of the neutrino
charge radius and the magnetic moment at the squared four momentum transfer
$Q^2=0$ obtained from the recent experiments and calculate the neutrino
differential cross section of the neutrino-$^{12}$C scattering. We find that
the effect of the charge radius and the electric dipole form factor is very
small, but the role of the magnetic dipole form factor is sensitive to $Q^2$
and becomes sizable at small momentum transfer.
