  Several authors have pointed out that the scalar-mediated interaction of
neutrinos in a neutriophilic two-Higgs-doublet model (nu2HDM) can be as strong
as electromagnetic interaction [1-3]. We show that the coupling constants of
neutrino-scalar interaction are actually restricted to be y_i < 1.5 x 10^{-3}
by supernova neutrino observation, and further constrained to be y_i < 2.3 x
10^{-4} by precision measurements of acoustic peaks of the cosmic microwave
background. Based on the energy-loss argument for supernova cores, we derive a
slightly more restrictive bound y_i < 3.5 x 10^{-5}. Therefore, the nu2HDM has
lost its spirit of explaining tiny Dirac neutrino masses while keeping neutrino
Yukawa couplings of order one.
