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. ; Comment: accepted by MNRAS; 14 pages