  We study the properties of the relativistic, steady, axisymmetric, low
angular momentum, inviscid, advective, geometrically thin accretion flow in a
Kerr-Taub-NUT (KTN) spacetime which is characterized by the Kerr parameter
($a_{\rm k}$) and NUT parameter ($n$). Depending on $a_{\rm k}$ and $n$ values,
KTN spacetime represents either a black or a naked singularity. We solve the
governing equations that describe the relativistic accretion flow in KTN
spacetime and obtain all possible global transonic accretion solutions around
KTN black hole in terms of the energy $({\cal E})$ and angular momentum
$(\lambda)$ of the flow. We identify the region of the parameter space in
$\lambda-{\cal E}$ plane that admits the flow to possess multiple critical
points for KTN black hole. We examine the modification of the parameter space
due to $a_{\rm k}$ and $n$ and find that the role of $a_{\rm k}$ and $n$ in
determining the parameter space is opposite to each other. This clearly
indicates that the NUT parameter $n$ effectively mitigates the effect of black
hole rotation in deciding the accretion flow structure. Further, we calculate
the maximum disc luminosity ($L_{\rm max}$) corresponding to the accretion
solutions around the KTN black hole and for a given set of $a_{\rm k}$ and $n$.
In addition, we also investigate all possible flow topologies around the naked
singularity and find that there exists a region around the naked singularity
which remains inaccessible to the flow. We study the critical point properties
for naked singularities and find that the flow possesses maximum of four
critical points. Finally, we obtain the parameter space for multiple critical
points for naked singularity and find that parameter space is shrunk and
shifted to lower $\lambda$ and higher ${\cal E}$ side as $a_{\rm k}$ is
increased which ultimately disappears.
