A relativistic mean-field hadronic model with a dark matter (DM) particle coupled to nucleons including short-range correlations (SRC) is applied to study neutron stars (NS). The lightest neutralino is chosen as the dark particle candidate, which interacts with nucleons by the exchange of Higgs bosons. A detailed thermodynamical analysis shows that the contribution of the DM fermions to the energy density of the matter composed by these particles and nucleons is completely dominated by the DM kinetic terms. The model reproduces satisfactorily the constraints on the mass-radius diagram obtained from the analysis of the combined data from the NICER mission, LIGO collaboration, and mass measurements from radio observations. We show that the SRC balance the reduction of the neutron star mass due to the DM component, and because of that the model is able to present more massive NS. We also present a study of the effect, in the NS mass-radius profiles, of the uncertainties in some bulk parameters related to the hadronic sector. We find that it is possible to generate parametrizations, with DM content, compatible with the recent astrophysical constraints and with the uncertainty in the symmetry energy slope obtained from the results reported by the updated lead radius experiment (PREX-2).