A connector comprising: a plug contact having conductivity, the plug contact including a tubular portion extending along a fitting axis in a Z direction with a recessed portion formed therein, and a flange extending from an end portion of the tubular portion in a direction orthogonal to the fitting axis; and an inner contact (18, 19, 28, 38) having conductivity, part of the inner contact being inserted in the recessed portion, whereby the inner contact includes a retaining portion (18A, 19A, 28A, 38A) 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 connecting portion (18C, 19C, 28C, 38C) extending in the direction orthogonal to the fitting axis and facing a rear surface of the flange, and a spring portion (18B, 19B, 28B, 38B) joining the connecting portion to the retaining portion so as to be elastically displaceable along the fitting axis, and wherein part of a connection object of sheet shape having a conductor (15C, 15E) exposed on at least one surface of the connection object is sandwiched between the rear surface of the flange of the plug contact and the connecting portion of the inner contact in a direction along the fitting axis, the rear surface of the flange makes contact with a front surface of the connection object, the connecting portion makes contact with a rear surface of the connection object and an elastic pressing force acting in the +Z direction is applied to the connecting portion (18C, 19C, 28C, 38C) by the spring portion (18B, 19B, 28B, 38B) of the inner contact (18, 19, 28, 38) such that the front surface on the +Z direction side of the sheet-shaped connection object 15 is pressed against the rear surface of the flange 13B of the plug contact 13, while a rear surface on the -Z direction side of the sheet-shaped connection object 15 is pressed against the front surface of the connecting portion (18C, 19C, 28C, 38C) of the inner contact (18, 19, 28, 38), whereby the plug contact is electrically connected to the conductor directly when the conductor is exposed on the front surface of the connection object, and the plug contact is electrically connected to the conductor via the inner contact (18, 19, 28, 38) when the conductor is exposed on the rear surface of the connection object. a plug contact having conductivity, the plug contact including a tubular portion extending along a fitting axis in a Z direction with a recessed portion formed therein, and a flange extending from an end portion of the tubular portion in a direction orthogonal to the fitting axis; and an inner contact (18, 19, 28, 38) having conductivity, part of the inner contact being inserted in the recessed portion, whereby the inner contact includes a retaining portion (18A, 19A, 28A, 38A) 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 connecting portion (18C, 19C, 28C, 38C) extending in the direction orthogonal to the fitting axis and facing a rear surface of the flange, and a spring portion (18B, 19B, 28B, 38B) joining the connecting portion to the retaining portion so as to be elastically displaceable along the fitting axis, and wherein part of a connection object of sheet shape having a conductor (15C, 15E) exposed on at least one surface of the connection object is sandwiched between the rear surface of the flange of the plug contact and the connecting portion of the inner contact in a direction along the fitting axis, the rear surface of the flange makes contact with a front surface of the connection object, the connecting portion makes contact with a rear surface of the connection object and an elastic pressing force acting in the +Z direction is applied to the connecting portion (18C, 19C, 28C, 38C) by the spring portion (18B, 19B, 28B, 38B) of the inner contact (18, 19, 28, 38) such that the front surface on the +Z direction side of the sheet-shaped connection object 15 is pressed against the rear surface of the flange 13B of the plug contact 13, while a rear surface on the -Z direction side of the sheet-shaped connection object 15 is pressed against the front surface of the connecting portion (18C, 19C, 28C, 38C) of the inner contact (18, 19, 28, 38), whereby the plug contact is electrically connected to the conductor directly when the conductor is exposed on the front surface of the connection object, and the plug contact is electrically connected to the conductor via the inner contact (18, 19, 28, 38) when the conductor is exposed on the rear surface of the connection object.