The Hall effect on an MHD dynamo driven by shear is studied. As with many turbulent transitions in purely hydrodynamic shear flows, whether a dynamo is generated or not must be treated in the framework of a subcritical transition problem, for which dynamical systems theory is useful. We focus on the steady-state solution that seems to be at the edge of basin of attraction of dynamo turbulence, and derive its behavior at high Reynolds numbers by matched asymptotic expansion. The structure of the solution is described by the interaction between the mean field and current sheets. Its overall framework is somewhat similar to that of mean field theory, but it does not require any artificial assumptions for closure.