  The rotation curve of the Milky Way is commonly used to estimate the local
dark matter density $\rho_{{\rm DM},\odot}$. However, the estimates are subject
to the choice of the distribution of baryons needed in this type of studies. In
this work we explore several Galactic mass models that differ in the
distribution of baryons and dark matter, in order to determine $\rho_{{\rm
DM},\odot}$. For this purpose we analyze the precise circular velocity curve
measurement of the Milky Way up to $\sim 25$ kpc from the Galactic centre
obtained from Gaia DR2 [1]. We find that the estimated value of $\rho_{{\rm
DM},\odot}$ stays robust to reasonable changes in the spherical dark matter
halo. However, we show that $\rho_{{\rm DM},\odot}$ is affected by the choice
of the model for the underlying baryonic components. In particular, we find
that $\rho_{{\rm DM},\odot}$ is mostly sensitive to uncertainties in the disk
components of the Galaxy. We also show that, when choosing one particular
baryonic model, the estimate of $\rho_{{\rm DM},\odot}$ has an uncertainty of
only about $10\%$ of its best-fit value, but this uncertainty gets much bigger
when we also consider the variation of the baryonic model. In particular, the
rotation curve method does not allow to exclude the presence of an additional
very thin component, that can increase $\rho_{{\rm DM},\odot}$ by more than a
factor of 8 (the thin disk could even be made of dark matter). Therefore, we
conclude that exclusively using the rotation curve of the Galaxy is not enough
to provide a robust estimate of $\rho_{{\rm DM},\odot}$. For all the models
that we study without the presence of an additional thin component, our
resulting estimates of the local dark matter density take values in the range
$\rho_{{\rm DM},\odot} \simeq \text{0.3--0.4}\,\mathrm{GeV/cm^3}$, consistent
with many of the estimates in the literature.
