  Using the well established principles of Lorentz invariance, CP and CPT
symmetry, and quantum statistics we do a model-independent study of effects of
possible non-standard couplings of (Dirac and Majorana) neutrinos. The study is
sensitive to the different quantum statistical properties of the Dirac and
Majorana neutrinos which, contrary to neutrino-mediated processes of lepton
number violation, could lead to observable effects not suppressed by the small
ratios of neutrino and heavier particle masses. For processes with a
neutrino-antineutrino pair of the same flavor in the final state, we formulate
the ``Dirac Majorana confusion theorem (DMCT)'' showing why it is normally very
difficult to observe the different behaviour of both kinds of neutrinos in
experiments if they have only the standard model (SM)-like left-handed vector
couplings to gauge bosons. We discuss deviations from the confusion theorem in
the presence of non-standard neutrino interactions, allowing to discover or
constrain such novel couplings. We illustrate the general results with two
chosen examples of neutral current processes, $Z \to \nu \, \overline{\nu}$ and
$\mathcal{P}_i \to \mathcal{P}_f \, \nu \, \overline{\nu}$ (with
$\mathcal{P}_{i,f}$ denoting pseudoscalar mesons, such as $B,K,\pi$). Our
analysis shows that using 3-body decays the presence of non-standard
interactions can not only be constrained but one can also distinguish between
Dirac and Majorana neutrino possibilities.
