  We study an impact of asymmetric fermionic dark matter on neutron star
properties, including tidal deformability, mass, radius, etc. We present the
conditions at which dark matter particles tend to form a compact structure in a
core of the star or create an extended halo around it. We show that compact
core of dark matter leads to a decrease of the total gravitational mass and
tidal deformability compared to a pure baryonic star, while presence of a dark
matter halo increases those observable quantities. By imposing an existing
astrophysical and gravitational wave constraints set by LIGO/Virgo
Collaboration together with the recent results on the spatial distribution of
dark matter in the Milky Way we determine a new upper limit on the mass and
fraction of dark matter particles inside compact stars. Furthermore, we show
that the formation of an extended halo around a NS is incompatible with the
GW170817 tidal deformability constraint.
