  Let $\Omega$ be an arbitrary bounded semi-Reinhardt domain in
$\mathbb{C}^{m+n}$. We show that for $m \geq 2$, if a Hankel operator with an
anti-holomorphic symbol is Hilbert-Schmidt on the Bergman space
$L_a^2(\Omega)$, then it must equal zero. This fact has previously been proved
for Reinhardt domains.
