  We propose here a specific criterion to address the existence or otherwise of
Kerr naked singularities, in terms of the precession of the spin of a test
gyroscope due to the frame dragging by the central spinning body. We show that
there is indeed an important characteristic difference in the behavior of gyro
spin precession frequency in the limit of approach to these compact objects,
and this can be used, in principle, to differentiate the naked singularity from
black hole. Specifically, if gyroscopes are fixed all along the polar axis upto
the horizon of a Kerr black hole, the precession frequency becomes arbitrarily
high, blowing up as the event horizon is approached. On the other hand, in the
case of naked singularity, this frequency remains always finite and
well-behaved. Interestingly, this behavior is intimately related to and is
governed by the geometry of the ergoregion in each of these cases which we
analyze here. One intriguing behavior that emerges is, in the Kerr naked
singularity case, the Lense-Thirring precession frequency ($\Omega_{\rm LT}$)
of the gyroscope due to frame-dragging effect decreases as ($\Omega_{\rm
LT}\propto r$) after reaching a maximum, in the limit of $r= 0$, as opposed to
$r^{-3}$ dependence in all other known astrophysical cases.
