We use data from the first two dayside seasons of the Magnetospheric Multiscale (MMS) mission to study current systems associated with quasi-perpendicular bow shocks of generator type. We have analyzed 154 MMS bow shock crossings near the equatorial plane. We compute the current density during the crossings and conclude that the component perpendicular to the shock normal (J⊥) is consistent with a pileup of the interplanetary magnetic field (IMF) inside the magnetosheath. For predominantly southward IMF, we observe a component Jn parallel (antiparallel) to the normal for GSM Y > 0 (<0), and oppositely directed for northward IMF. This indicates current closure across the equatorial magnetosheath, and it is observed for IMF clock angles near 0(ring operator) and 180(ring operator). To our knowledge, these are the first observational evidence for bow shock current closure across the magnetosheath. Since we observe no clear signatures of |J⊥| decreasing toward large |Y| we suggest that the main region of current closure is further tailward, outside MMS probing region. For IMF clock angles near 90(ring operator), we find indications of the current system being tilted toward the north-south direction, obtaining a significant Jz component, and we suggest that the current closes off the equatorial plane at higher latitudes where the spacecraft are not probing. The observations are complicated for several reasons. For example, variations in the solar wind and the magnetospheric currents and loads affect the closure, and Jn is distributed over large regions, making it difficult to resolve inside the magnetosheath proper.