Whether neutrinos are Majorana or Dirac particles is an open question. Theoretically, it is also possible that neutrinos are pseudo-Dirac, which are fundamentally Majorana fermions, but essentially act like Dirac fermions in most experimental settings, due to small active-sterile mass splitting. Such small values of mass splitting can only be accessed via active-sterile oscillations over an astrophysical baseline, or via decays of neutrinos over a cosmological time scale. In this talk, we will use the multi-messenger observation of high-energy neutrino sources and the excess extragalactic radio background to probe two different regimes of the pseudo-Dirac neutrino parameter space.