  The time-dependent $CP$ asymmetry in $B^0 \to K_{\rm res} \gamma \to \pi^+
\pi^- K^0_{\scriptscriptstyle S} \gamma$ is sensitive to the photon
polarisation in the quark level process $b \to s \gamma$. While this
polarisation is predominantly left-handed in the standard model, it could be
modified by the existence of new physics contributions that may possess
different $CP$ properties. In this paper, we derive the $CP$ violation formulae
for $B^0 \to K_{\rm res} \gamma \to \pi^+ \pi^- K^0_{\scriptscriptstyle S}
\gamma$ including the most dominant intermediate states. We propose a new
observable that could be measured in a time-dependent amplitude analysis of
$B^0 \to \pi^+ \pi^- K^0_{\scriptscriptstyle S} \gamma$ decays, providing a
stringent contraint on the photon polarisation. We discuss the future prospects
for obtaining such constraints from measurements at Belle II and LHCb.
