Spin-dependent tunneling between a layer-wise antiferromagnet grown on a ferromagnetic substrate and a ferromagnetic tip electrode was studied using spin-polarized scanning tunneling microscopy (Sp-STM). The systems under investigation consist of thin Mn films deposited on an Fe(001) substrate, a vacuum barrier, and an Fe-coated STM electrode. The asymmetry of the tunnel currents, measured over a wide voltage range, is nonzero but small, only a few percent and exhibits a change of sign as a function of voltage. Surface states are found to contribute significantly to the tunnel current only for small tip-distances. The comparison with model calculations for ballisitc transport supports that the current asymmetry can be attributed mainly to the symmetry breaking at the surface, that is to the surface layer of the Mn film.