Many observations show a difference between the pressure parallel and perpendicular to the magnetic field. Thus it is reasonable to study the Petschek reconnection mechanism for the set of equations allowing for pressure anisotropy. We study the simplest case of so-called Petschek shocks, where the Alfvén discontinuity and the slow shock degenerate to one discontinuity. More specifically, we consider switch-off shocks, where the magnetic field on the downstream side vanishes in lowest order, so that the plasma is isotropic on that side.