We present the nonlocal kinetic linear stability analysis of the self-consistent isotropic collisionless plasma equilibrium with strongly stretched magnetic field lines (the so-called modified Harris sheet) with respect to the tearing mode, which provides the onset of laminar reconnection in the system. The stability problem is solved using the finite element technique and the drift-kinetic description for the electron species with additional averaging over the bounce motion of the trapped electrons. The mode is found unstable for ion-to-electron temperature ratios typical for the tail current sheet of Earth's magnetosphere when this sheet is sufficiently long, so that the electrons leaving it may be treated as transient particles. Comparison of the theory with earlier fluid modeling shows that the onset of reconnection is controlled by the Hall effect and a purely kinetic effect arising from different responses of the trapped and transient electrons. Geophysical implications such as the formation of the near-Earth neutral line and thin current sheets during substorms are discussed.