  In the literature, the Newman-Janis algorithm (NJA) has been widely used to
construct stationary and axisymmetric spacetimes to describe rotating black
holes. In addition, it has been recently shown that the general stationary and
axisymmetric spacetime generated through NJA allows the complete separability
of the null geodesic equations. In fact, the Hamilton-Jacobi equation in this
spacetime is also separable if one of the metric functions is additively
separable. In this work, we further study the conditions for a separable
Klein-Gordon equation in such a general spacetime. The relations between the
NJA spacetime and other parameterized axially symmetric spacetimes in the
literature are also discussed.
