  Using an adapted version of the SGRID code, we construct for the first time
consistent quasi-equilibrium configurations for a binary system consisting of
two neutron stars in which each is admixed with dark matter. The stars are
modelled as a system of two non-interacting fluids minimally coupled to
gravity. For the fluid representing baryonic matter the SLy equation of state
is used, whereas the second fluid, which corresponds to dark matter, is
described using the equation of state of a degenerate Fermi gas. We consider
two different scenarios for the distribution of the dark matter. In the first
scenario the dark matter is confined to the core of the star, whereas in the
second scenario the dark matter extends beyond the surface of the baryonic
matter, forming a halo around the baryonic star. The presence of dark matter
alters the star's reaction to the companion's tidal forces, which we
investigate in terms of the coordinate deformation and mass shedding
parameters. The constructed quasi-equilibrium configurations mark the first
step towards consistent numerical-relativity simulations of dark matter admixed
neutron star binaries.
