A battery module is disclosed, which includes: a multiplicity of battery cells; a printed circuit board with a first series-connector with a first pad area and a second pad area, and a second series-connector with a third pad area and a fourth pad area; a cross-connector, which connects the first series-connector between the first pad area and the second pad area with the second series-connector between the third pad area and the fourth pad area; and a sensor configured to detect a cross-current at the cross-connector. The first contact electrode of a first battery cell is connected with the first pad area. The second contact electrode of a second battery cell is connected with the second pad area. The first contact electrode of a third battery cell is connected with the third pad area. The second contact electrode of a fourth battery cell is connected with the fourth pad area.