We derive the off-shell nilpotent and absolutely anticommuting
Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for the
dynamical non-Abelian 2-form gauge theory within the framework of geometrical
superfield formalism. We obtain the (anti-) BRST invariant coupled Lagrangian
densities that respect the above nilpotent symmetry transformations. We
discuss, furthermore, this (anti-) BRST invariance in the language of the
superfield formalism. One of the novel features of our investigation is the
observation that, in addition to the horizontality condition, we have to invoke
some other physically relevant restrictions to deduce the exact (anti-) BRST
symmetry transformations for all the fields of the topologically massive
non-Abelian gauge theory.Comment: LaTeX file, 8 pages, typos fixed in some equations, journal-versio