A connector includes an inner contact inserted in a recessed portion of a plug contact and composed of a bent wire spring, the inner contact having an elastically displaceable contact portion contacting the plug contact and an elastically displaceable pressing portion, part of a connection object having a flexible conductor exposed on at least one surface thereof being sandwiched between the pressing portion and an inner surface of the recessed portion, the inner surface of the recessed portion and the pressing portion contacting a front surface and a rear surface of the connection object, respectively, the plug contact being electrically connected to the flexible conductor directly when the flexible conductor is exposed on the front surface of the connection object, the plug contact being electrically connected to the flexible conductor via the inner contact when the flexible conductor is exposed on the rear surface of the connection object.