  We discuss neutrino sector in models with two Higgs doublet and one singlet
scalar fields under local $U(1)_{L_\alpha- L_\beta}$ symmetry. A neutrino mass
matrix is formulated for these models where the matrix is generated via type-I
seesaw mechanism introducing right-handed neutrinos. The neutrino mass matrix
has more degrees of freedom compared to minimal scenarios which have only one
new scalar field, but its structure is still restricted by the symmetry. Then
it is find that sum of neutrino mass can be lower than minimal scenarios and it
is easier to satisfy observed constraints. In addition, we can fit neutrino
data for $U(1)_{L_e - L_{\mu(\tau)}}$ cases which are disfavored in minimal
models. Furthermore, some correlations among sum of neutrino mass and CP
violating phases are still found although we have more free parameters.
