We study a Kerr-like black hole and naked singularity in perfect fluid dark matter ( PFDM ) .
The critical value of spin parameter a _ { c } is presented to differentiate the black hole from naked singularity .
It is seen that for any fixed value of dark matter parameter \alpha the rotating object is black hole if a \leq a _ { c } and naked singularity if a > a _ { c } .
Also for -2 \leq \alpha < 2 / 3 the size of the black hole horizons decrease whereas for 2 / 3 < \alpha it increases .
We also study spin precession frequency of a test gyroscope attached to stationary observer to differentiate a black hole from naked singularity in PFDM .
For the black hole , spin precession frequency blows up as the observer reaches the central object while for naked singularity it remains finite except at the ring singularity .
Moreover , we study Lense-Thirring precession for a Kerr-like black hole and geodetic precession for Schwarzschild black hole in PFDM .
To this end , we have calculated the Kepler frequency ( KF ) , the vertical epicyclic frequency ( VEF ) , and the nodal plane precession frequency ( NPPF ) .
Our results show that , the PFDM parameter \alpha significantly affects those frequencies .
This difference can be used by astrophysical observations in the near future to shed some light on the nature of dark matter .