Humans show an involuntary tendency to copy other people's actions. Although automatic imitation builds rapport and affiliation between individuals, we do not copy actions indiscriminately. Instead, copying behaviors are guided by a selection mechanism, which inhibits some actions and prioritizes others. To date, the neural underpinnings of the inhibition of automatic imitation and differences between the sexes in imitation control are not well understood. Previous studies involved small sample sizes and low statistical power, which produced mixed findings regarding the involvement of domain-general and domain-specific neural architectures. Here, we used data from Experiment 1 (N = 28) to perform a power analysis to determine the sample size required for Experiment 2 (N = 50; 80% power). Using independent functional localizers and an analysis pipeline that bolsters sensitivity, during imitation control we show clear engagement of the multiple-demand network (domain-general), but no sensitivity in the theory-of-mind network (domain-specific). Weaker effects were observed with regard to sex differences, suggesting that there are more similarities than differences between the sexes in terms of the neural systems engaged during imitation control. In summary, neurocognitive models of imitation require revision to reflect that the inhibition of imitation relies to a greater extent on a domain-general selection system rather than a domain-specific system that supports social cognition.