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.
