  Let $K$ be an imaginary quadratic field and $K_\infty$ be the
$\mathbf{Z}_p^2$-extension of $K$. Answering a question of Ahmed and Lim, we
show that the Pontryagin dual of the Selmer group associated to a supersingular
polarized abelian variety admits an algebraic functional equation. The proof
uses the theory of $\Gamma$-system developed by Lai, Longhi, Tan and Trihan. We
also show the algebraic functional equation holds for Sprung's chromatic Selmer
groups of supersingular elliptic curves along $K_\infty$.
