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Magnetospheres at ion kinetic scales, or mini-magnetospheres, possess unusual features as predicted by numerical simulations. However, there are practically no data on the subject from space observations and the data which are available are far too incomplete. In this paper we describe the results of a laboratory experiment on the interaction of plasma flow with a magnetic dipole with parameters such that the ion inertial length is larger than the size of an observed magnetosphere. A detailed structure of the non-coplanar or out-of-plane component of the magnetic field has been obtained in the meridian plane. The independence of this component on dipole moment reversal, as was reported in a previous work, has been verified. In the tail distinct lobes and a central current sheet have been observed. It was found that lobe regions adjacent to boundary layer are dominated by a non-coplanar component of magnetic field. Tail-ward oriented electric current in the plasma associated with that component appears to be equal to the ion current in the upstream part of magnetosphere and in the tail current sheet implying that electrons are stationary in those regions while the ions flow by. The data obtained strongly support the proposed model of mini-magnetosphere based on two-fluid effects as described by the Hall term. [ABSTRACT FROM AUTHOR]