  We revisit slow rotating black hole (BH) solutions in Chern-Simons modified
gravity (CSMG) by considering perturbative solution about Schwarzschild BH. In
particular, the case when nondynamical CSMG with noncanonical CS scalar is
considered. We provide a new solution different from the previously obtained
one \cite{Konno:2007ze} which we refer to as KMT model. The present solution
accounts for frame dragging effect which includes not only radial dependence as
in the KMT. Nevertheless, it reduces to KMT as a particular case. We show that
the tidal gravitational force (Kretschmann invariant) associated to the present
solution contains a term of order $1/r^3$ additional to Schwarzschild but
absent from directional divergence, unlike KMT model which diverges along the
axis of symmetry. We derive the corresponding circular velocity of a massive
test particle in which the KMT velocity is recovered in addition to an extra
term $\propto r$. We investigate possible constraints on KMT and the present
solutions from the observed rotation curve of UGC11455 galaxy as an example. We
show that perturbation solutions cannot physically explain the flattening of
galactic rotation curves.
