  We calculate the neutrino-electron elastic scattering cross section,
extending the results previously obtained in arXiv:1702.05721v2, in the
presence of generic new interactions that take into account all the effects
caused by finite neutrino masses. We address the potential significance of a
heavy neutrino sector during precision measurements, particularly for tau
neutrinos scattering with masses in the MeV range, for which the existing upper
bounds on $|U_{\tau 4}|^2$ would result in conceivably measurable
contributions. Finally, we comment on the possibility to distinguish between
Dirac and Majorana neutrinos, including the analysis of the new emerging
parameters and its application to illustrative model-dependent scenarios.
