In this work the neutral-current scattering cross-section for neutrinos on electrons is calculated assuming that a massive Dirac neutrino is characterized by a phenomenological parameters, a charge radius < r²> and the right-handed currents are present in the framework of a Left-Right symmetric model (LR). Using the CHARM II result for the charge radius of the muon-neutrino |< r²>|＜6.0×10^-33cm², we place a bound on -7.9×10^-33cm²≤< r²>_LR≤7.9×10^-33cm². We discuss the relationship between the electron neutral couplings g^Ve_V and g^Ve_A and the LR model parameters. We also estimate a bound on the heavy massive neutral vector boson mass M_ZR＞650GeV of the LR model. These results have never been reported in the literature before and could have practical or theoretical interest, such as in the case of the neutrinos produced in core-collapse supernova explosions, that is to say, right-handed Dirac neutrinos emission from supernova core v_Le^-→v_Re^-.