We consider Cluster observations of events with an intense current density (>5 nA/m2) in the magnetotail current sheet. We use measurements by Cluster mission in the central magnetotail (X <− 16 RE, |Y|<10 RE, and |Bx|<10 nT) in the 2003 season when the spacecraft separation was about ∼300 km. For this season, when Cluster can probe very small scale currents, we collect the statistics of observations of strong current densities jy (in GSM coordinate system) and compare curlometer data with plasma parameters. The most intense currents are observed under disturbed conditions (plasma flow vx>300 km/s). We introduce the parameter vD/vTi (where vD=jy/ene, ne is an electron density, and vTi is a proton thermal velocity) and show that cases with vD/vTi∼1 correspond to the most intense currents observed in the vicinity of the reconnection regions. The comparison of electron and proton velocities demonstrates that electron often carry almost the entire current measured by a curlometer technique. The strong electron temperature anisotropy Te∥/Te⊥>1.2 corresponds to large magnitudes of By component of the magnetic field. We conclude that intense current sheets are often characterized by significant (more than 30%) contribution of electron curvature currents to the cross‐tail current. The comparison of observations and models shows that the electron anisotropy level is likely controlled by competition of two processes: the electron scattering on fluctuations generated by fire‐hose instability and the acceleration in sheared magnetic field configurations. We also suggest that current sheets embedded into the strong plasma flows (vx/vTi>0.1) can be balanced by ion flow anisotropy.