  When neutrino masses arise from the exchange of neutral heavy leptons, as in
most seesaw schemes, the effective lepton mixing matrix $N$ describing neutrino
propagation is non-unitary, hence neutrinos are not exactly orthonormal. New CP
violation phases appear in $N$ that could be confused with the standard phase
$\delta_{\text{CP}}$ characterizing the three neutrino paradigm. We study the
potential of the long-baseline neutrino experiment DUNE in probing CP violation
induced by the standard CP phase in the presence of non-unitarity. In order to
accomplish this we develop our previous formalism, so as to take into account
the neutrino interactions with the medium, important in long baseline
experiments such as DUNE. We find that the expected CP sensitivity of DUNE is
somewhat degraded with respect to that characterizing the standard unitary
case. However the effect is weaker than might have been expected thanks mainly
to the wide neutrino beam. We also investigate the sensitivity of DUNE to the
parameters characterizing non-unitarity. In this case we find that there is no
improvement expected with respect to the current situation, unless the near
detector setup is revamped.
