  We studied a simple model of hidden sector consists of a Dirac fermion $\chi$
and a spontaneously broken $U(1)_s$ symmetry. The dark sector is connected to
the Standard Model(SM) via three righthanded SM singlet neutrinos, $N_R$'s, and
the kinetic mixing between $U(1)_s$ and $U(1)_Y$. A mixing between the scalar
$\phi$ that breaks $U(1)_s$ and the SM Higgs boson, $H$, is implemented via the
term $\phi^\dagger \phi H^\dagger H$ and this provides a third connection to
the SM. Integrating out the $N_R$ at a high scale not only gives the active
neutrinos, $\nu$, masses but generates effective Dirac type of couplings
between $\nu$ and $\chi$. This changes the usual Type-I seesaw results for
active neutrino masses and makes $\chi$ behave like a sterile neutrino even
though its origin is in the hidden sector. $\chi$ is also split into a pair of
Majorana fermions. The amount of splitting depends on the parameters. If the
lighter of the pair has a mass around keV, its lifetime is longer than the age
of the universe and it can be a warm dark matter candidate. Signatures of
$\chi$ in high precision Kurie plots of nuclei $\beta$ decays and low energy
neutrino nuclei coherent scatterings are discussed. The model also induces new
invisible $Z$ decay modes that can be searched for in future Z factories.
