The neural basis of multitasking costs is subject to continuing debate. Cognitive theories assume that the overlap of task representations may lead to between‐task crosstalk in concurrent task processing and thus requires cognitive control. Recent research suggests that modality‐based crosstalk contributes to multitasking costs, involving central overlap of modality‐specific representations. Consistently increased costs for specific modality pairings (visual‐vocal and auditory‐manual vs. visual‐manual and auditory‐vocal) were demonstrated (modality‐compatibility effect), which were recently linked to representational overlap in the auditory cortex. However, it remains unclear whether modality‐based crosstalk emerges from overlapping patterns of global brain connectivity and whether resolving it requires additional involvement of cognitive control as reflected in the fronto‐parietal control network. This preregistered functional imaging study investigates these questions in 64 healthy, young human adults. Specifically, we focus on the modality‐compatibility effect in multitasking by employing functional connectivity (FC) analysis. First, we tested the FC similarity FC dissimilarity between the single‐task networks. Second, we compared the strength of the control network in whole‐brain FC between dual tasks. We found no evidence for differences in FC dissimilarities of single‐task networks between modality pairings and no additional involvement of the control network during dual tasks by comparing the global connectivity. However, unregistered post hoc connectivity analysis revealed the first evidence for a correlation of the (behavioral) modality‐compatibility effect with local FC. This effect was locally restricted to FC between lateral frontal and sensory auditory regions, consistent with the modality‐based crosstalk assumption. More generally, the findings suggest that robust behavioral differences in multitasking are not necessarily related to global functional connectivity differences but might be related to functionally specific local connectivity changes.