  We study the key factor to determine the dimensionless spin parameter
$j\equiv cJ/(GM^2)$ of different kinds of uniformly rotating compact stars,
including the traditional neutron stars, hyperonic neutron stars, and hybrid
stars, and check the reliability of the results on various types of equations
of state of dense matter. The equations of state from the relativistic mean
field theory and the MIT bag model are adopted to simulate compact stars.
Numerical calculations of rigidly rotating neutron stars are performed using
the RNS code in the framework of general relativity by solving the Einstein
equations for stationary axis-symmetric spacetime. The crust structure of
compact stars is found to be a key factor to determine the maximum value of the
spin parameter $j_{\rm max}$. For the stars with inclusion of the crust,
$j_{\rm max}\sim 0.7$ is sustained for various kinds of compact stars with
$M>0.5 M_{\odot}$, and is found to be insensitive to the mass of star and
selected equations of state. For the traditional neutron stars, hyperonic
neutron stars and hybrid stars without crust structure, the value $j_{\rm max}$
lies in the range of $[0.7, 1.0]$. Thus, not $j>0.7$ but $j>1$ could be treated
as the candidate criterion to distinguish the strange quark stars from the
other kinds of compact stars. Furthermore, a universal formula
$j=0.48(f/f_K)^3-0.42(f/f_K)^2+0.63(f/f_K)$ is suggested to calculate the spin
parameter at any rotational frequency for all kinds of compact stars with crust
structure and $M>0.5M_{\odot}$.
