We present Mars Global Surveyor measurements of bipolar out-of-plane magnetic fields at current sheets in Mars' magnetosphere. These signatures match predictions from simulations and terrestrial observations of collisionless magnetic reconnection, and could similarly indicate differential ion and electron motion and the resulting Hall current systems near magnetic X lines. Thus, these observations may represent passages through or very near reconnection diffusion regions at Mars. Out of 28 events found at 400 km altitude with well-defined current sheet orientations, 26 have magnetic fields consistent with the expected polarities of Hall fields near diffusion regions. For these events, we find an average ratio of Hall field to main field of 0.51 ± 0.13, and an average ratio of normal to main field (reconnection rate) of 0.16 ± 0.09, consistent with terrestrial observations of reconnection. These events do not consistently correlate with the location of crustal fields or with IMF reversals, indicating that magnetic field draping alone (perhaps enhanced by high solar wind dynamic pressure) may generate current sheets capable of reconnection. For some events, we observe field-aligned electrons that may carry parallel currents that close the Hall current loop. Electron distributions around current sheets often indicate magnetic connection to the collisional exosphere. For crossings sunward of the X line, we usually observe an electron flux minimum at the current sheet, consistent with the resulting closed magnetic structure. For crossings antisunward of the X line, we do not observe flux minima, consistent with field lines open downstream. Collisionless reconnection, if common at Mars, could represent a significant atmospheric loss process.