A connector comprising: a plug contact having conductivity and including a tubular portion and a flange, the tubular portion extending along a fitting axis and having a recessed portion formed therein, and the flange extending from an end portion of the tubular portion in a direction perpendicular to the fitting axis; a bottom insulator including a support surface that extends in the direction perpendicular to the fitting axis; and an inner contact having conductivity and disposed on the support surface, part of the inner contact being inserted in the recessed portion, wherein the inner contact includes: a retaining portion retained in the recessed portion and making contact with an inner surface of the recessed portion to be electrically connected to the plug contact; a flat plate portion being elastically deformable, joined to the retaining portion, extending in the direction perpendicular to the fitting axis, and facing a bottom surface of the flange; a plurality of top surface-side projections projecting toward the bottom surface of the flange from a top surface of the flat plate portion; and a plurality of bottom surface-side projections projecting toward the support surface from a bottom surface of the flat plate portion separately at positions different from positions of the top surface-side projections, and part of a connection object of sheet type having a conductor (15C, 15E) exposed on at least one surface of the connection object is sandwiched in a direction along the fitting axis between the bottom surface of the flange of the plug contact and the top surface-side projections of the inner contact, the bottom surface of the flange makes contact with a top surface of the connection object, and the top surface-side projections make contact with a bottom surface of the connection object, whereby the plug contact is electrically connected to the conductor directly when the conductor is exposed on the top surface of the connection object, and the plug contact is electrically connected to the conductor via the inner contact when the conductor is exposed on the bottom surface of the connection object. a plug contact having conductivity and including a tubular portion and a flange, the tubular portion extending along a fitting axis and having a recessed portion formed therein, and the flange extending from an end portion of the tubular portion in a direction perpendicular to the fitting axis; a bottom insulator including a support surface that extends in the direction perpendicular to the fitting axis; and an inner contact having conductivity and disposed on the support surface, part of the inner contact being inserted in the recessed portion, wherein the inner contact includes: a retaining portion retained in the recessed portion and making contact with an inner surface of the recessed portion to be electrically connected to the plug contact; a flat plate portion being elastically deformable, joined to the retaining portion, extending in the direction perpendicular to the fitting axis, and facing a bottom surface of the flange; a plurality of top surface-side projections projecting toward the bottom surface of the flange from a top surface of the flat plate portion; and a plurality of bottom surface-side projections projecting toward the support surface from a bottom surface of the flat plate portion separately at positions different from positions of the top surface-side projections, and part of a connection object of sheet type having a conductor (15C, 15E) exposed on at least one surface of the connection object is sandwiched in a direction along the fitting axis between the bottom surface of the flange of the plug contact and the top surface-side projections of the inner contact, the bottom surface of the flange makes contact with a top surface of the connection object, and the top surface-side projections make contact with a bottom surface of the connection object, whereby the plug contact is electrically connected to the conductor directly when the conductor is exposed on the top surface of the connection object, and the plug contact is electrically connected to the conductor via the inner contact when the conductor is exposed on the bottom surface of the connection object.