  If neutrinos get mass via the seesaw mechanism the mixing matrix describing
neutrino oscillations can be effectively non-unitary. We show that in this case
the neutrino appearance probabilities involve a new CP phase, phi, associated
to non-unitarity. This leads to an ambiguity in extracting the "standard"
three--neutrino phase delta_CP, which can survive even after neutrino and
antineutrino channels are combined. Its existence should be taken into account
in the planning of any oscillation experiment aiming at a robust measurement of
delta_CP.
