  We discuss the toplogical sigma model on an orbifold target space. We
describe the moduli space of classical minima for computing correlation
functions involving twisted operators, and show, through a detailed computation
of an orbifold of ${\bf CP}^1$ by the dihedral group $D_{4},$ how to compute
the complete ring of observables. Through this procedure, we compute all the
rings from dihedral ${\bf CP}^1$ orbifolds; we note a similarity with rings
derived from perturbed $D-$series superpotentials of the $A-D-E$ classification
of $N = 2$ minimal models. We then consider ${\bf CP}^2/D_4,$ and show how the
techniques of topological-anti-topological fusion might be used to compute
twist field correlation functions for nonabelian orbifolds.
