On the bow shock in front of Earth flows current due to the curl of interplanetary magnetic field across the shock. It is uncertain whether the bow shock current closes on the magnetopause, into the ionosphere along magnetic field lines, or both. We present simultaneous observations from MMS, AMPERE, and DMSP during a period of strong $B_y$, weakly negative $B_z$, and small $B_x$. This IMF orientation should lead to current flowing mostly south-north on the shock. AMPERE shows current poleward of the Region 1 currents flowing into the northern polar cap and out of the south, consistent with bow shock current closing along open field lines; a DMSP flyover confirms that this current is poleward of the convection reversal boundary. Additionally, we investigate bow shock current closure for these conditions using an MHD simulation. We conclude that the evidence points to partial closure of bow shock current through the ionosphere.