  The current observational properties of neutron stars have not definitively
ruled out the possibility of dark matter. In this study, we primarily focus on
exploring correlations between the dark matter model parameters and different
neutron star properties using a rich set of EOSs. We adopt a two-fluid approach
to calculate the properties of neutron stars. For the nuclear matter EOS, we
employ several realistic EOS derived from the relativistic mean field model
(RMF), each exhibiting varying stiffness and composition. In parallel, we look
into the dark matter EOS, considering fermionic matter with repulsive
interaction described by a relativistic mean field Lagrangian. A reasonable
range of parameters is sampled meticulously. Interestingly, our results reveal
a promising correlation between the dark matter model parameters and stellar
properties, particularly when we ignore the uncertainties in the nuclear matter
EOS. However, when introducing uncertainties in the nuclear sector, the
correlation weakens, suggesting that the task of conclusively constraining any
particular dark matter model might be challenging using global properties
alone, such as mass, radius, and tidal deformability. Notably, we find that
dark-matter admixed stars tend to have higher central baryonic density,
potentially allowing for non-nucleonic degrees of freedom or direct Urca
processes in stars with lower masses. There is also a tantalizing hint
regarding the detection of stars with the same mass but different surface
temperatures, which may indicate the presence of dark matter. With our robust
and extensive dataset, we delve deeper and demonstrate that even in the
presence of dark matter, the semi-universal C-Love relation remains intact.
