A conductor rail module for distributing and a corresponding connection module for tapping a direct current distributed along a mounting rail is described. The connection module comprises a housing whose electrically insulating rear section is connected or connectable to the mounting rail in a form-fit manner. A front section of the housing has a plurality of electrically insulating transverse struts extending transversely to a longitudinal direction of the conductor rail module. Furthermore, the conductor rail module comprises at least two conductor rails extending in the longitudinal direction in the housing between the rear section and the front section, which conductor rails are configured to contact the connection modules for distributing the direct current through a gap between the transverse struts when the connection modules are in a position mounted on the conductor rail module.