We classify neutrino mass generation mechanisms by focusing on combinations of new Yukawa coupling matrices with leptons. We find that a wide class of models for neutrino masses can be excluded if a decay of h to l l' is discovered in the current or future collider experiments. In particular, simple models of Majorana neutrino masses cannot be compatible with the observation of the decay. It is also found that some of the simple models to generate masses of Dirac neutrinos radiatively can be compatible with a significant rate of the decay.