In mouse primary visual cortex (V1), local excitatory connections are more prevalent, stronger and larger between neurons that share similar functional response features. However, the extent to which rules for local cortical connection specificity shape visual responses, as well as full details relating structure and function both remain unknown. We considered whether complex responses to plaid stimuli in mouse V1 could be explained by one of two alternative connectivity schemes: whether local connections are aligned with simple feedforward visual properties, or whether local connections group across feedforward visual properties. Using a combined experimental and computational approach, we found that responses to plaid stimuli in mouse V1 were best explained by a connectivity scheme which binds multiple feedforward visual properties. Our results show that feature binding can occur through a recurrent mechanism not requiring feedforward convergence; such a mechanism is consistent with visual responses in mouse V1.