  We discuss gauge models incorporating $\mu-\tau$ flavored CP symmetry (called
CP$^{\mu\tau}$ in the text) in combination with $L_\mu-L_\tau$ invariance to
understand neutrino mixings and discuss their phenomenological implications. We
show that viable leptogenesis in this setting requires that the lightest
right-handed neutrino mass must be between $10^9-10^{12}$ GeV and for effective
two hierarchical right-handed neutrinos, leptogenesis takes place only in a
narrower range of $5\times 10^{10}-10^{12}$ GeV. A multi-Higgs realization of
this idea implies that there must be a pseudoscalar Higgs boson with mass less
than 300 GeV. Generically, the vev alignment problem can be naturally avoided
in our setting.
