  In this paper we consider the role that worldsheet instantons in the
heterotic string could play in spin-statistics violations. Such violations are
nonperturbative in the string tension and so would not appear in the spacetime
effective action, producing a unique signature of string theory and the details
of compactification. By performing a Bogomol'nyi transformation it is shown
that there are no instanton solutions in the simplest model proposed by Harvey
and Liu, but it is conjectured that more sophisticated models may yield
solutions. If such instantons do exist, their effect might be measured by
upcoming experiments.
