  We study decoherence effects on mixing among three generations of neutrinos.
We show that in presence of a non--diagonal dissipation matrix, both Dirac and
Majorana neutrinos can violate the $CPT$ symmetry and the oscillation formulae
depend on the parametrization of the mixing matrix. We reveal the $CP$
violation in the transitions preserving the flavor, for a certain form of the
dissipator. In particular, the $CP$ violation affects all the transitions in
the case of Majorana neutrinos, unlike Dirac neutrinos which still preserve the
$CP$ symmetry in one of the transitions flavor preserving. This theoretical
result shows that decoherence effects, if exist for neutrinos, could allow to
determine the neutrino nature and to test fundamental symmetries of physics.
Next long baseline experiments could allow such an analysis. We relate our
study with experiments by using the characteristic parameters and the
constraints on the elements of the dissipation matrix of current experiments.
