  The nucleon form factors in free space are usually thought to be modified
when a nucleon is bound in a nucleus or immersed in a nuclear medium. We
investigate effects of the density-dependent axial and weak-vector form factors
on the electro-neutrino ($\nu_e$) and anti-electro-neutrino $({\bar \nu_e})$
reactions via neutral current (NC) for a nucleon in nuclear medium or $^{12}$C.
For the density-dependent form factors, we exploit the quark-meson-coupling
(QMC) model, and apply them to the $\nu_e$ and ${\bar \nu_e}$ induced reactions
by NC. About 12% decrease of the total cross section by $\nu_e$ reaction on the
nucleon is obtained at normal density, $\rho = \rho_0 \sim 0.15 {fm}^{-3} $, as
well as about 18% reduction of total ${\nu}_e$ cross section on $^{12}$C, by
the modification of the weak form factors of the bound nucleon.
  However, similarly to the charged current reaction, effects of the nucleon
property change in the ${\bar \nu}_e$ reaction reduce significantly the cross
sections about 30% for the nucleon in matter and $^{12}$C cases. Such a large
asymmetry in the ${\bar \nu}_e$ cross sections is addressed to originate from
the different helicities of ${\bar \nu}_e$ and ${\nu}_e$.
