  The behavior of spin-half particles is discussed in the 3 + 1-dimensional
constant curvature black hole (CCBH) spacetime. We use Schwarzschild-like
coordinates, valid outside the black hole event horizon. The constant time
surfaces corresponding to the time-like Killing vector are degenerate at the
black hole event horizon and also along an axis. We write down the Dirac
equation in this spacetime using Newman-Penrose formalism which is not easily
separable unlike that in the Kerr metric. However, with a particular choice of
basis system the equation is separable and we obtain the solutions. We discuss
the structural difference in the Dirac equation in the CCBH spacetime with that
in the Kerr geometry, due to difference in the corresponding spacetime metric,
resulting complexity arised in separation in the earlier case.
