  We show the existence of a global anomaly in the one-loop graphs of N=2
string theory, defined by sewing tree amplitudes, unless spacetime
supersymmetry is imposed. The anomaly is responsible for the non-vanishing
maximally helicity violating amplitudes. The supersymmetric completion of the
N=2 string spectrum is formulated by extending the previous cohomological
analysis with an external spin factor; the target space-time spin-statistics of
these individual fields in a selfdual background are compatible with previous
cohomological analysis as fields of arbitrary spin may be bosonized into one
another. We further analyze duality relations between the open and closed
string amplitudes and demonstrate this in the supersymmetric extension of the
target space-time theory through the insertion of zero-momentum operators.
