  Accurate determination of the local dark matter density is important for
understanding the nature and distribution of dark matter in the universe. This
requires that the local velocity distribution is characterised correctly. Here,
we present a kinematic study of 16,276 SEGUE G-type dwarf stars in the solar
neighbourhood, with which we determine the shape of the velocity ellipsoid in
the meridional plane. We separate our G-dwarf stars based on their [Fe/H] and
[alpha/Fe] abundances and infer the local velocity distribution independently
for each sub-sample using a maximum-likelihood method that accounts for
possible contaminants. We show by constructing vertical Jeans models that the
different sub-samples yield consistent results only when we allow the velocity
ellipsoid in the disk to be tilted, demonstrating that the common assumption of
decoupled radial and vertical motions in the disk is incorrect. Further, we
obtain that the tilt of the velocity ellipsoid is consistent among the
different sub-samples. We find that increase in the tilt with height is well
described by the relation alpha_tilt = (-0.90 +- 0.04) arctan(|z|/R_sun) -
(0.01 +- 0.005), which is close to alignment with the spherical coordinate
system and hence a velocity ellipsoid pointing to the Galactic centre. We also
confirm earlier findings that the sub-samples behave almost isothermally with
both radial and vertical velocity dispersion approximately constant with
height. We conclude that the coupling between radial and vertical motion
captured in the velocity ellipsoid tilt cannot be ignored when considering
dynamical models of the solar neighbourhood. In a subsequent paper, we will
develop a new modelling scheme informed by these results and make an improved
determination of the local dark matter density.
