  We propose a complex extension of $\mu\tau$ permutation antisymmetry in the
neutrino Majorana matrix $M_\nu$. The latter can be realized for the Lagrangian
by appropriate CP transformations on the neutrino fields. The resultant form of
$M_\nu$ is shown to be simply related to that with a complex (CP) extension of
$\mu\tau$ permutation symmetry, with identical phenomenological consequences,
though their group theoretic origins are quite different. We investigate those
consequences in detail for the minimal seesaw induced by two strongly
hierarchical right-chiral neutrinos $N_1$ and $N_2$ with the result that the
Dirac phase is maximal while the two Majorana phases are either 0 or $\pi$. We
further provide an uptodate discussion of the $\beta\beta0\nu$ process
vis-a-vis ongoing and forthcoming experiments. Finally, a thorough treatment is
given of baryogenesis via leptogenesis in this scenario, primarily with the
assumption that the lepton asymmetry produced by the decays of $N_1$ only
matters here with the asymmetry produced by $N_2$ being washed out. Tight upper
and lower bounds on the mass of $N_1$ are obtained from the constraint of
obtaining the correct observed range of the baryon asymmetry parameter and the
role played by $N_2$ is elucidated thereafter. The mildly hierarchical
right-chiral neutrino case (including the quasidegenerate possibility) is
discussed in an Appendix.
