  A possible manifestation of an additional light gauge boson $A^\prime$, named
as Dark Photon, associated with a group $U(1)_{\rm B-L}$ is studied in neutrino
electron scattering experiments. The exclusion plot on the coupling constant
$g_{\rm B-L}$ and the dark photon mass $M_{A^\prime}$ is obtained. It is shown
that contributions of interference term between the dark photon and the
Standard Model are important. The interference effects are studied and compared
with for data sets from TEXONO, GEMMA, BOREXINO, LSND as well as CHARM II
experiments. Our results provide more stringent bounds to some regions of
parameter space.
