  We study CP-violation effects when neutrinos are present in dense matter,
such as outside the proto-neutron star formed in a core-collapse supernova.
Using general arguments based on the Standard Model, we confirm that there are
no CP-violating effects at the tree level on the electron neutrino and
anti-neutrino fluxes in a core-collapse supernova. On the other hand
significant effects can be obtained for muon and tau neutrinos even at the tree
level. We show that CP violating effects can be present in the supernova
electron (anti)neutrino fluxes as well, if muon and tau neutrinos have
different fluxes at the neutrinosphere. Such differences could arise due to
physics beyond the Standard Model, such as the presence of flavor-changing
interactions.
