At a low activity comet the plasma is distributed in an asymmetric way. The hybrid simulation code Amitis is used to look at the spatial evolution of ion velocity distribution functions (VDFs), from the upstream solar wind to within the comet magnetosphere where the solar wind is heavily mass-loaded by the cometary plasma. We find that the spatial structures of the ions and fields form a highly asymmetric, half-open induced magnetosphere. The VDFs of solar wind and cometary ions vary drastically for different locations in the comet magnetosphere. The shape of the VDFs differ for different species. The solar wind protons show high anisotropies that occasionally resemble partial rings, in particular at small cometocentric distances. A second, decoupled, proton population is also found. Solar wind alpha particles show similar anisotropies, although less pronounced and at different spatial scales. The VDFs of cometary ions are mostly determined by the structure of the electric field. We perform supplementary dynamic particle backtracing to understand the flow patterns of solar wind ions that lead to these anisotropic distributions. This tracing is needed to understand the origin of cometary ions in a given part of the comet magnetosphere. The particle tracing also aids in interpreting observed VDFs and relating them to spatial features in the electric and magnetic fields of the comet environment.