  The slow rotation of Kerr-NUT spacetime is explored by taking into account
the linear form of rotation and NUT parameters in the dynamical Chern-Simon
gravity theory, which can be formulated from a scalar field describing the
background. We show that in the absence of the potential scalar field, the
metric potential does not respect the effect of the NUT parameter, although the
scalar field is affected by the rotation and NUT parameters. Consequently,
unlike the gradually spinning black hole solution outlined in
\cite{Alexander:2009tp}, the mixed component of the metric potential,
encompassing both rotational and NUT parameters, doesn't make a contribution at
the primary level of the initial perturbation.
