Abstract: Scalar (fermion) dark matter with mass in the MeV range coupled to ordinary neutrinos and another fermion (scalar) is motivated by scenarios that establish a link between radiatively generated neutrino masses and the dark matter relic density. With such a coupling, cosmic supernova neutrinos, on their way to us, could resonantly interact with the background (lark matter particles, giving rise to a dip in their redshift-integrated spectra. Current and future neutrino detectors, such as Super-Kamiokande. LENA and HyperKamiokande, could be able to detect this distortion.