New and more reliable distances and proper motions of a large number of stars in the Tycho-Gaia Astrometric Solution ( TGAS ) catalogue allow to calculate the local matter density distribution more precisely than earlier .

We devised a method to calculate the stationary gravitational potential distribution perpendicular to the Galactic plane by comparing the vertical probability density distribution of a sample of observed stars with the theoretical probability density distribution computed from their vertical coordinates and velocities .
We applied the model to idealised test stars and to the real observational samples .
Tests with two mock datasets proved that the method is viable and provides reasonable results .

Applying the method to TGAS data we derived that the total matter density in the Solar neighbourhood is 0.09 \pm 0.02 ~ { } \text { M } _ { \odot } \text { pc } ^ { -3 } being consistent with the results from literature .
The matter surface density within |z| \leq 0.75 ~ { } \text { kpc } is 42 \pm 4 ~ { } \text { M } _ { \odot } \text { pc } ^ { -2 } .
This is slightly less than the results derived by other authors but within errors is consistent with previous estimates .
Our results show no firm evidence for significant amount of dark matter in the Solar neighbourhood .
However , we caution that our calculations at |z| \leq 0.75 kpc rel on an extrapolation from the velocity distribution function calculated at |z| \leq 25 pc .
This extrapolation can be very sensitive to our assumption that the stellar motions are perfectly decoupled in R and z , and to our assumption of equilibrium .
Indeed , we find that \rho ( z ) within |z| \leq 0.75 kpc is asymmetric with respect to the Galactic plane at distances |z| = 0.1 - 0.4 kpc indicating that the density distribution may be influenced by density perturbations .