  A seesaw mechanism in an extra-dimension, known as the split seesaw
mechanism, provides a natural way to realize a splitting mass spectrum of
right-handed neutrinos. It leads to one keV sterile neutrino as a dark matter
candidate and two heavy right-handed neutrinos being responsible for
leptogenesis to explain the observed baryon asymmetry of the Universe. We study
models based on $A_4$ flavor symmetry in the context of the split seesaw
mechanism. It is pointed out that most of known $A_4$ flavor models with three
right-handed neutrinos being $A_4$ triplet suffer from a degeneracy problem for
the bulk mass terms, which disturbs the split mechanism for right-handed
neutrino mass spectrum. Then we construct a new $A_4$ flavor model to work in
the split seesaw mechanism. In the model, the experimentally observed neutrino
masses and mixing angles can be realized from both type I+II seesaw
contributions. The model predicts the $\mu-\tau$ symmetry in the neutrino mass
matrix at the leading order, resulting in the vanishing $\theta_{13}$ and
maximal $\theta_{23}$. The flavor symmetry $A_4$ is broken via the flavon
vacuum alignment which can be obtained from the orbifold compactification. The
model can be consistent with all data of neutrino oscillation experiments,
cosmological discussions of dark matter abundance, leptogenesis, and recent
astrophysical data.
