  We derive the off-shell nilpotent Becchi-Rouet-Stora-Tyutin (BRST) and
anti-BRST symmetry transformations for {\it all} the fields of a free Abelian
2-form gauge theory by exploiting the geometrical superfield approach to BRST
formalism. The above four (3 + 1)-dimensional (4D) theory is considered on a
(4, 2)-dimensional supermanifold parameterized by the four even spacetime
variables x^\mu (with \mu = 0, 1, 2, 3) and a pair of odd Grassmannian
variables \theta and \bar\theta (with \theta^2 = \bar\theta^2 = 0, \theta
\bar\theta + \bar\theta \theta = 0). One of the salient features of our present
investigation is that the above nilpotent (anti-)BRST symmetry transformations
turn out to be absolutely anticommuting due to the presence of a Curci-Ferrari
(CF) type of restriction. The latter condition emerges due to the application
of our present superfield formalism. The actual CF condition, as is well-known,
is the hallmark of a 4D non-Abelian 1-form gauge theory. We demonstrate that
our present 4D Abelian 2-form gauge theory imbibes some of the key signatures
of the 4D non-Abelian 1-form gauge theory. We briefly comment on the
generalization of our supperfield approach to the case of Abelian 3-form gauge
theory in four (3 + 1)-dimensions of spacetime.
