  The Kerr-Taub-NUT spacetime in the Kaluza-Klein theory represents a localized
stationary and axisymmetric object in four dimensions from the Kaluza-Klein
viewpoint. That is, it harbors companion electromagnetic and dilaton fields,
thereby showing up the signature of the extra fifth dimension. We explore the
separability structure of this spacetime and show that the Hamilton-Jacobi
equation for geodesics admits the complete separation of variables only for
massless geodesics. This implies the existence of the hidden symmetries in the
spacetime, which are generated by the conformal Killing tensor. Using a simple
trick built up on a conformally related metric (an "effective" metric) with the
Killing tensor, we construct the explicit expression for the conformal Killing
tensor.
