Thirty rapid crossings of the magnetotail current sheet by the Cluster spacecraft during July-October 2001 at a geocentric distance of 19 RE are examined in detail to address the structure of the current sheet. We use four-point magnetic field measurements to estimate electric current density; the current sheet spatial scale is estimated by integration of the translation velocity calculated from the magnetic field temporal and spatial derivatives. The local normal-related coordinate system for each case is defined by the combining Minimum Variance Analysis (MVA) and the curlometer technique. Numerical parameters characterizing the plasma sheet conditions for these crossings are provided to facilitate future comparisons with theoretical models. Three types of current sheet distributions are distinguished: center-peaked (type I), bifurcated (type II) and asymmetric (type III) sheets. Comparison to plasma parameter distributions show that practically all cases display non-Harris-type behavior, i.e. interior current peaks are embedded into a thicker plasma sheet. The asymmetric sheets with an off-equatorial current density peak most likely have a transient nature. The ion contribution to the electric current rarely agrees with the current computed using the curlometer technique, indicating that either the electron contribution to the current is strong and variable, or the current density is spatially or temporally structured.