  If massive neutrinos are Majorana particles, then the lepton number should be
violated in nature and neutrino-antineutrino oscillations $\nu^{}_\alpha
\leftrightarrow \overline{\nu}^{}_\beta$ (for $\alpha, \beta = e, \mu, \tau$)
will definitely take place. In the present paper, we study the properties of CP
violation in neutrino-antineutrino oscillations with the non-unitary leptonic
flavor mixing matrix, which is actually a natural prediction in the canonical
seesaw model due to the mixing between light and heavy Majorana neutrinos. The
oscillation probabilities $P(\nu^{}_\alpha \to \overline{\nu}^{}_\beta)$ and
$P(\overline{\nu}^{}_\alpha \to \nu^{}_\beta)$ are derived, and the CP
asymmetries ${\cal A}^{}_{\alpha \beta} \equiv [P(\nu^{}_\alpha \to
\overline{\nu}^{}_\beta) - P(\overline{\nu}^{}_\alpha \to
\nu^{}_\beta)]/[P(\nu^{}_\alpha \to \overline{\nu}^{}_\beta) +
P(\overline{\nu}^{}_\alpha \to \nu^{}_\beta)]$ are also calculated. Taking into
account current experimental bounds on the leptonic unitarity violation, we
show that the CP asymmetries induced by the non-unitary mixing parameters can
significantly deviate from those in the limit of a unitary leptonic flavor
mixing.
