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 being provided in its interior with a recessed portion, and the flange extending from a base end of the tubular portion in a direction orthogonal to the fitting axis; an inner contact (18, 28) having conductivity and being supported while having part of the inner contact inserted in the recessed portion; and a housing (12, 22) retaining the plug contact, wherein the housing includes a restriction portion (17H, 27E) that is disposed in the recessed portion of the plug contact and is configured to restrict rotation of the inner contact, the inner contact includes a first contacting portion that makes contact with an inner surface of the recessed portion to be electrically connected to the plug contact, a second contacting portion that makes contact with the inner surface of the recessed portion on an opposite side from the first contacting portion across the fitting axis and at a position closer to the base end of the recessed portion than the first contacting portion is, a third contacting portion extending in a direction orthogonal to the fitting axis and facing the flange, and a restricted portion that faces in an opposite direction from the second contacting portion and makes contact with the restriction portion at a position closer to the base end of the recessed portion than the second contacting portion is, and part of a connection object (15, 25) of sheet shape having a conductor (15B, 15D, 25B, 25D) exposed on at least one surface of the connection object is sandwiched between a bottom surface of the flange of the plug contact and the third contacting portion of the inner contact in a direction along the fitting axis, the bottom surface of the flange makes contact with a top surface of the connection object, and the third contacting portion makes 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 being provided in its interior with a recessed portion, and the flange extending from a base end of the tubular portion in a direction orthogonal to the fitting axis; an inner contact (18, 28) having conductivity and being supported while having part of the inner contact inserted in the recessed portion; and a housing (12, 22) retaining the plug contact, wherein the housing includes a restriction portion (17H, 27E) that is disposed in the recessed portion of the plug contact and is configured to restrict rotation of the inner contact, the inner contact includes a first contacting portion that makes contact with an inner surface of the recessed portion to be electrically connected to the plug contact, a second contacting portion that makes contact with the inner surface of the recessed portion on an opposite side from the first contacting portion across the fitting axis and at a position closer to the base end of the recessed portion than the first contacting portion is, a third contacting portion extending in a direction orthogonal to the fitting axis and facing the flange, and a restricted portion that faces in an opposite direction from the second contacting portion and makes contact with the restriction portion at a position closer to the base end of the recessed portion than the second contacting portion is, and a first contacting portion that makes contact with an inner surface of the recessed portion to be electrically connected to the plug contact, a second contacting portion that makes contact with the inner surface of the recessed portion on an opposite side from the first contacting portion across the fitting axis and at a position closer to the base end of the recessed portion than the first contacting portion is, a third contacting portion extending in a direction orthogonal to the fitting axis and facing the flange, and a restricted portion that faces in an opposite direction from the second contacting portion and makes contact with the restriction portion at a position closer to the base end of the recessed portion than the second contacting portion is, and part of a connection object (15, 25) of sheet shape having a conductor (15B, 15D, 25B, 25D) exposed on at least one surface of the connection object is sandwiched between a bottom surface of the flange of the plug contact and the third contacting portion of the inner contact in a direction along the fitting axis, the bottom surface of the flange makes contact with a top surface of the connection object, and the third contacting portion makes 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.