  We propose a complex extension of mixed $\mu\tau$ antisymmetry in the
neutrino Majorana mass matrix $M_\nu$. This can be implemented in the
Lagrangian by a generalized CP transformation (labeled by a mixing parameter
$\theta$) on the left-chiral flavor neutrino fields. We investigate its
implications for leptonic CP violation and neutrino phenomenology in general.
Interestingly, the $\mu\tau$ mixing parameter $\theta$ gets correlated with the
Dirac CP phase $\delta$ and the atmospheric mixing angle $\theta_{23}$ through
an analytical relation. In general, for arbitrary $\theta$, both $\theta_{23}$
and $\delta$ are nonmaximal. We discuss the corresponding results for the CP
asymmetry parameter $A_{\mu e}$ in neutrino oscillation experiments. For a
nonmaximal $\delta$, one of the two Majorana phases is different from $0$ or
$\pi$, thereby leading to nonvanishing Majorana CP violation with observable
consequences for the neutrinoless double beta ($\beta\beta0\nu$) decay process.
We numerically work out in detail the predictions for that process in relation
to various ongoing and forthcoming experiments. We also work out the
predictions of our scheme on flavor flux ratios at neutrino telescopes. While
exact CP transformed $\mu\tau$ interchange antisymmetry ($\theta=\pi/2$) leads
to an exact equality among those ratios, taking a value $0.5$, a tiny deviation
can cause a drastic change in them. Careful measurement of these flux ratios in
future will further constrain the parameter $\theta$.
