A case having an electrical connector terminal for connection to a mating connector terminal, the case comprising a case body and a cover, the case body including a cover attachment rectangular frame that is tubular or socket-shaped, that has a substantially rectangular cross section, and that is elastically deformable, a cover attachment structure allowing the cover, which has a substantially rectangular outline, to be pressed into the cover attachment rectangular frame from an opening at an end of the cover attachment rectangular frame by a predetermined distance and to be attached to a predetermined cover attachment position; and engagement portions that are disposed in the cover attachment rectangular frame and that prevent forward movement and separation of the cover attached to the cover attachment position, wherein the engagement portions protrude or bulge inward from one of two pairs of opposite inner wall surfaces (117, 118) of the cover attachment rectangular frame in such a way that a minimum distance Wxt between the engagement portions before the cover is attached is smaller than a corresponding side-to-side dimension Hx of the cover, characterized by: a stopper that is disposed in the cover attachment rectangular frame and that prevents the cover from being excessively pressed into the cover attachment rectangular frame; and in that: in the cover attachment rectangular frame before the cover is attached, a distance Wx, at the cover attachment position, between the one of the two pairs of opposite inner wall surfaces on which the engagement portions are disposed is greater than the corresponding side-to-side dimension Hx of the cover, and a distance Wy, at the cover attachment position, between the other of the two pairs of opposite inner wall surfaces on which the engagement portions are not disposed is smaller than a corresponding side-to-side dimension Hy of the cover, and wherein, in a state in which the cover is pressed into the cover attachment rectangular frame and attached to the cover attachment position, a distance between the opposite inner wall surfaces on which the engagement portions are not disposed is increased by the cover, and thereby the inner wall surfaces firmly press the cover and the cover attachment rectangular frame is deformed so that a distance between the opposite inner wall surfaces on which the engagement portions are disposed is reduced. a stopper that is disposed in the cover attachment rectangular frame and that prevents the cover from being excessively pressed into the cover attachment rectangular frame; and in that: in the cover attachment rectangular frame before the cover is attached, a distance Wx, at the cover attachment position, between the one of the two pairs of opposite inner wall surfaces on which the engagement portions are disposed is greater than the corresponding side-to-side dimension Hx of the cover, and a distance Wy, at the cover attachment position, between the other of the two pairs of opposite inner wall surfaces on which the engagement portions are not disposed is smaller than a corresponding side-to-side dimension Hy of the cover, and wherein, in a state in which the cover is pressed into the cover attachment rectangular frame and attached to the cover attachment position, a distance between the opposite inner wall surfaces on which the engagement portions are not disposed is increased by the cover, and thereby the inner wall surfaces firmly press the cover and the cover attachment rectangular frame is deformed so that a distance between the opposite inner wall surfaces on which the engagement portions are disposed is reduced. in the cover attachment rectangular frame before the cover is attached, a distance Wx, at the cover attachment position, between the one of the two pairs of opposite inner wall surfaces on which the engagement portions are disposed is greater than the corresponding side-to-side dimension Hx of the cover, and a distance Wy, at the cover attachment position, between the other of the two pairs of opposite inner wall surfaces on which the engagement portions are not disposed is smaller than a corresponding side-to-side dimension Hy of the cover, and wherein, in a state in which the cover is pressed into the cover attachment rectangular frame and attached to the cover attachment position, a distance between the opposite inner wall surfaces on which the engagement portions are not disposed is increased by the cover, and thereby the inner wall surfaces firmly press the cover and the cover attachment rectangular frame is deformed so that a distance between the opposite inner wall surfaces on which the engagement portions are disposed is reduced.