In this study, we analyse the kinematics and dynamics of a homogeneous sample of red clump stars, selected from the second Gaia data release catalogue in the direction of the Galactic poles, at five different positions in the plane. The level of completeness of the sample at heights between 0.6 and 3.5 kpc was asserted through a comparison with the 2 Micron All Sky Survey catalogue. We show that both the density distribution and velocity dispersion are significantly more perturbed in the north than in the south in all analysed regions of our Galactic neighbourhoods. We provide a detailed assessment of these north-south asymmetries at large heights, which can provide useful constraints for models of the interaction of the Galactic disc with external perturbers. We proceeded to evaluate how such asymmetries could affect determinations of the dynamical matter density under equilibrium assumptions. We find that a Jeans analysis delivers relatively similar vertical forces and integrated dynamical surface densities at large heights above the plane in both hemispheres. At these heights, the densities of stars and gas are very low and the surface density is largely dominated by dark matter (DM), which allows us to estimate, separately in the north and in the south, the local dark matter density derived under equilibrium assumptions. In the presence of vertical perturbations, such values should be considered as an upper limit. This Jeans analysis yields values of the local dark matter density above 2 kpc, namely, ρDM ∼ 0.013 M⊙ pc−3 (∼0.509 GeV cm−3) in the perturbed northern hemisphere and ρDM ∼ 0.010 M⊙ pc−3 (∼0.374 GeV cm−3) in the much less perturbed south. As a comparison, we determine the local dark matter density by fitting a global phase-space distribution to the data. We end up with a value in the range of ρDM ∼ 0.011−0.014 M⊙ pc−3, which is in global agreement with the Jeans analysis. These results call for the further development of non-equilibrium methods with the aim of obtaining a more precise estimate for the dynamical matter density in the Galactic disc.