The Einstein-Cartan-Liouville (ECL) theory, which unifies the Einstein-Cartan (EC) theory and Einstein-Liouville (EL) theory, is considered, by understanding as the relativistic kinetic theory associating the spin effects in space-time manifold endowed with torsion. The self-consistency of this ECL theory is confirmed in terms of two conservation laws for momentum and spin. The charged case of the ECL theory -the Einstein-Cartan-Maxwell-Liouville (ECML) theory- is also investigated through the constants of motion. It is applied to the Petrov type-$G_4$ VIII cosmological and the static spherically symmetric astrophysical models under two kinds of prescription to determine the torsion components. It is obtained that the matter parts agree with the geometrical ones in these models.