  It is proven that up to possible surface terms, the only non-vanishing
momentum-dependent amplitudes for the self-dual N=2 string in $R^{2,2}$ are the
tree-level two and three-point functions, and the only non-vanishing
momentum-independent amplitudes are the one-loop partition function and the
tree-level two and four-point functions. The calculations are performed using
the topological prescription developed in an earlier paper with Vafa. As in
supersymmetric non-renormalization theorems, the vanishing proof is based on a
relationship between the zero-momentum dilaton and axion.
