  The Rankin-Selberg integral of Kohnen and Skoruppa produces the Spin
$L$-function for holomorphic Siegel modular forms of genus two. In this paper,
we reinterpret and extend their integral to apply to arbitrary cuspidal
automorphic representations of $\mathrm{PGSp}_4$. We show that the integral is
related to a non-unique model and analyze it using the approach of
Piatetski-Shapiro and Rallis.
