  In this paper, we investigate the properties of the Lense-Thirring precession
frequency and periastron precession of the relativistic bound orbits in slowly
rotating naked singularity spacetimes. We show that the precession frequencies
of a stationary test gyroscope are quite unique in slowly rotating naked
singularity spacetimes, and therefore, one can easily distinguish them from the
slowly rotating Kerr black hole spacetime. On the other hand, we also show that
in slowly rotating Joshi-Malafarina-Narayan (JMN1) naked singularity spacetime,
negative precession of the timelike bound orbits is allowed which is not
possible in Kerr and slowly rotating null naked singularity spacetimes.
