A connector comprising: a plug contact (13, 33) having a conductive property and including a recessed portion (13C, 33C) extending along a fitting axis; an inner contact (18, 28) having a conductive property and inserted in the recessed portion; and a bottom insulator (17, 27) including a projection (17C, 27C) extending along the fitting axis and inserted in the recessed portion, wherein the inner contact (18, 28) includes a contact portion that is elastically displaceable in a direction perpendicular to the fitting axis and makes contact with the plug contact in the recessed portion, a projection contacting portion that is elastically displaceable in a direction perpendicular to the fitting axis and makes contact with a lateral surface of the projection in the recessed portion, and a pressing portion that is elastically displaceable in a direction perpendicular to the fitting axis and faces an inner surface of the recessed portion, and a part of a connection object of sheet type having a flexible conductor (15D, 15F) exposed on at least one surface of the connection object is sandwiched between the pressing portion and the inner surface of the recessed portion in a direction perpendicular to the fitting axis, the inner surface of the recessed portion makes contact with a top surface of the connection object, and the pressing portion makes contact with a bottom surface of the connection object, whereby the plug contact (13, 33) is electrically connected to the flexible conductor directly when the flexible conductor is exposed on the top surface of the connection object, and the plug contact (13, 33) is electrically connected to the flexible conductor via the inner contact (18, 28) when the flexible conductor is exposed on the bottom surface of the connection object. a plug contact (13, 33) having a conductive property and including a recessed portion (13C, 33C) extending along a fitting axis; an inner contact (18, 28) having a conductive property and inserted in the recessed portion; and a bottom insulator (17, 27) including a projection (17C, 27C) extending along the fitting axis and inserted in the recessed portion, wherein the inner contact (18, 28) includes a contact portion that is elastically displaceable in a direction perpendicular to the fitting axis and makes contact with the plug contact in the recessed portion, a projection contacting portion that is elastically displaceable in a direction perpendicular to the fitting axis and makes contact with a lateral surface of the projection in the recessed portion, and a pressing portion that is elastically displaceable in a direction perpendicular to the fitting axis and faces an inner surface of the recessed portion, and a part of a connection object of sheet type having a flexible conductor (15D, 15F) exposed on at least one surface of the connection object is sandwiched between the pressing portion and the inner surface of the recessed portion in a direction perpendicular to the fitting axis, the inner surface of the recessed portion makes contact with a top surface of the connection object, and the pressing portion makes contact with a bottom surface of the connection object, whereby the plug contact (13, 33) is electrically connected to the flexible conductor directly when the flexible conductor is exposed on the top surface of the connection object, and the plug contact (13, 33) is electrically connected to the flexible conductor via the inner contact (18, 28) when the flexible conductor is exposed on the bottom surface of the connection object.