On the singular rank of a representation

Consider the reductive dual pair $({\text{S}}{{\text{p}}_{2n}},{{\text{O}}_{p,q}})$. We prove that if $\pi$ is a representation of ${\text{S}}{{\text{p}}_{2n}}$ coming from duality correspondence with some representation of ${{\text{O}}_{p,q}}$ then the wave front set of $\pi$ has rank $\leq p + q$. For $p + q < n$ this implies a result stated (but not proved) by Howe.