We show that current microlensing and dynamical observations of the Galaxy permit to set interesting constraints on the Dark Matter local density and profile slope towards the galactic centre . Assuming state-of-the-art models for the distribution of baryons in the Galaxy , we find that the most commonly discussed Dark Matter profiles ( viz . Navarro-Frenk-White and Einasto ) are consistent with microlensing and dynamical observations , while extreme adiabatically compressed profiles are robustly ruled out . When a baryonic model that also includes a description of the gas is adopted , our analysis provides a determination of the local Dark Matter density , \rho _ { 0 } = 0.20 - 0.56 \textrm { GeV / cm } ^ { 3 } at 1 \sigma , that is found to be compatible with estimates in the literature based on different techniques .