  We discuss various symmetry properties of the Lagrangian density of a four (3
+ 1)-dimensional (4D) free Abelian 2-form gauge theory within the framework of
Becchi-Rouet-Stora-Tyutin (BRST) formalism. The present free Abelian gauge
theory is endowed with a Curci-Ferrari type condition which happens to be a key
signature of the 4D non-Abelian 1-form gauge theory. In fact, it is due to the
above condition that the nilpotent BRST and anti-BRST symmetries of the theory
are found to be absolutely anticommuting in nature. For our present 2-form
gauge theory, we discuss the BRST, anti-BRST, ghost and discrete symmetry
properties of the Lagrangian densities and derive the corresponding conserved
charges. The algebraic structure, obeyed by the above conserved charges, is
deduced and the constraint analysis is performed with the help of the
physicality criteria where the conserved and nilpotent (anti-)BRST charges play
completely independent roles. These physicality conditions lead to the
derivation of the above Curci-Ferrari type restriction, within the framework of
BRST formalism, from the constraint analysis.
