This paper uses the steady state Vlasov theory to obtain an explicit description of the properties of thin current sheets in two space dimensions. The method is general; in particular, it is not restricted to local Maxwellian distribution functions. The treatment includes chaotic particle motion, and the plasma is treated as quasi-neutral. Such general equilibria are necessary for modeling observed structures in the Earth's magnetotail. In particular, this applies to thin current sheets embedded in wider sheets. Abandoning local Maxwellian distribution functions implies that the electric potential can no longer be transformed to zero such that additional efforts are required to include the electric field. Critical input parameters are the gyroscales of the different particle species and the ion/electron temperature ratio. The results illustrate how finite ion gyroscales affect the current sheet structure. Further aspects that are analyzed include the contributions of electrons and ions to the total current density, Hall currents, the occurrence of significant electric fields and the role of the ion/electron temperature ratio. The necessity of electric potentials in the self-consistent structure of thin current sheets of the present type may provide a link between the presence or formation of thin current sheets and auroral arcs.