  We consider groups G which have a cocompact, 3-manifold model for the
classifying space \underline{E}G. We provide an algorithm for computing the
rationalized equivariant K-homology of \underline{E}G. Under the additional
hypothesis that the quotient 3-orbifold \underline{E}G/G is geometrizable, the
rationalized K-homology groups coincide with the rationalized K-theory of the
reduced C*-algebra of G. We illustrate our algorithm on some concrete examples.
