  We study the non-monotonic Keplerian velocity profiles related to locally
non-rotating frames (LNRF) in the field of near-extreme braneworld Kerr black
holes and naked singularities in which the non-local gravitational effects of
the bulk are represented by a braneworld tidal charge $b$ and the 4D geometry
of the spacetime structure is governed by the Kerr-Newman geometry. We show
that positive tidal charge has a tendency to restrict the values of the black
hole dimensionless spin $a$ admitting existence of the non-monotonic Keplerian
LNRF-velocity profiles; the non-monotonic profiles exist in the black hole
spacetimes with tidal charge smaller than $b=0.41005$ (and spin larger than
$a=0.76808$). With decreasing value of the tidal charge (which need not be only
positive), both the region of spin allowing the non-monotonicity in the
LNRF-velocity profile around braneworld Kerr black hole and the velocity
difference in the minimum-maximum parts of the velocity profile increase
implying growing astrophysical relevance of this phenomenon.
