Dispersion relations are derived for collisionless tearing mode instabilities in the magnetotail in which the magnetic field passing through the current sheet connects to the ionosphere. In the absence of the conducting ionosphere, the presence of a component of the magnetic field normal to the current sheet large enough to magnetize the electrons stabilizes the current sheet against the tearing mode. It is shown, however, that height-integrated ionospheric conductivities in the 0.1- to 1.0-mho range are sufficient to allow the tearing mode instability to grow with e-folding times of several minutes. The effect of polarization currents is also investigated, and it is found that they are unlikely to have a significant effect. It is pointed out that the connection of the ionosphere to the current sheet would expose the ionosphere to the electric potentials that are generated during the explosive phase of the instability. These potentials may have a role in accelerating auroral electrons.