  In this paper, we study the prospects for determining the nature of neutrinos
in the context of a supersymmetric $B-L$ extension of the standard model by
using dark matter indirect detection signals and bounds on $N_{\text{eff}}$
from the cosmic microwave background data. The model contains two new dark
matter candidates whose dominant annihilation channels produce more neutrinos
than neutralino dark matter in the minimal supersymmetric standard model. The
photon and neutrino counts may then be used to discriminate between the two
models. If the dark matter comes from the B-L sector, its indirect signals and
impact on the cosmic microwave background can shed light on the nature of the
neutrinos. When the light neutrinos are of Majorana type, the indirect neutrino
signal from the Sun and the galactic center may show a prompt neutrino
box-feature, as well as an earlier cut-off in both neutrino and gamma ray
energy spectra. When the light neutrinos are of Dirac type, their contribution
to the effective number of neutrinos $N_{\text{eff}}$ is at a detectable level.
