  A class of Riemann-Cartan G\"odel-type space-times are examined in the light
of the equivalence problem techniques. The conditions for local space-time
homogeneity are derived, generalizing previous works on Riemannian G\"odel-type
space-times. The equivalence of Riemann-Cartan G\"odel-type space-times of this
class is studied. It is shown that they admit a five-dimensional group of
affine-isometries and are characterized by three essential parameters $\ell,
m^2, \omega$: identical triads ($\ell, m^2, \omega$) correspond to locally
equivalent manifolds. The algebraic types of the irreducible parts of the
curvature and torsion tensors are also presented.
