The ionization history of the universe in the presence of radiatively decaying neutrinos with masses between 30 eV and a few keV is studied. We consider a model in which most of the neutrinos decay into invisible particles at a rate t-1ν>>t-10, with t0 being the present age of the universe, while a small fraction of neutrinos, B, decay radiatively. We follow the evolution of the fraction of neutral hydrogen (H I), neutral helium (He I), and singly ionized helium (He II) in the diffuse intergalactic medium (IGM), taking into account the absorption of decay photons by hydrogen and helium in the diffuse IGM and the Lyα systems. The constraints on radiatively decaying neutrinos from the spectrum of cosmic background radiation, SN 1987A, the cooling of red giants, and the diffuse extragalactic background of photons are also considered. We derive the parameter space--spanned by the mass of the unstable neutrino mν, tν, and B--allowed by the Gunn-Peterson (GP) tests for H I, He I, and He II, the proximity effect, and Lyα emission at high redshifts. It is shown that the ionization state of the diffuse IGM, as required by the GP tests, can be explained without violating any other astrophysical or cosmological constraint on the model. We also investigate the implications of recently observed resonant neutral helium lines at z ~= 2 on the radiatively decaying neutrino scenario; this observation rules out almost all of the parameter space for neutrino masses >~50 eV.