  We analyze the neutrino phenomenology in an $SU(5)$ F-theory model with both
a visible sector and a twin hidden sector. At low energies, the strong and weak
scales of the two sectors may differ but the spectrum of states is described by
the MSSM (MSSM$^\prime$) in the visible (twin) sectors. What is special about
the model is that there are right-handed neutrinos which couple to both sectors
via Yukawa couplings. As a result, assuming 3 right-handed neutrinos with a
large mass much greater than the weak scale, at tree-level the seesaw mechanism
results in 3 massive Majorana neutrinos and 3 massless ones. The massless
neutrinos acquire mass via radiative corrections. In our analysis, the massless
neutrinos are predominantly active neutrinos, while the massive neutrinos are
predominantly sterile neutrinos. We fit the active neutrino masses and mixing
angles and discuss the phenomenology of the lightest sterile neutrino. Finally
we consider some possible scenarios for cosmology.
