  A precise determination of the local dark matter density and an accurate
control over the corresponding uncertainties are of paramount importance for
Dark Matter (DM) searches. Using very recent high-resolution numerical
simulations of a Milky Way like object, we study the systematic uncertainties
that affect the determination of the local dark matter density based on
dynamical measurements in the Galaxy. In particular, extracting from the
simulation with baryons the orientation of the Galactic stellar disk with
respect to the DM distribution, we study the DM density for an observer located
at $\sim$8 kpc from the Galactic center {\it on the stellar disk}, $\rho_0$.
This quantity is found to be always larger than the average density in a
spherical shell of same radius $\bar{\rho}_0$, which is the quantity inferred
from dynamical measurements in the Galaxy, and to vary in the range
$\rho_0/\bar{\rho}_0=1.01-1.41$. This suggests that the actual dark matter
density in the solar neighbourhood is on average 21\% larger than the value
inferred from most dynamical measurements, and that the associated systematic
errors are larger than the statistical errors recently discussed in the
literature.
