Theory of mind (ToM), or the ability to attribute mental states to oneself and others, is a core element of social cognition (SC). Even though its importance for social functioning in general, and neurodevelopmental disorders (NDDs), in particular, is well established, the links between ToM and other cognitive functions are not. Especially the familial underpinnings of such links remain unclear. Using a co-twin control design, we examined N = 311 twins (mean age M = 17.19 years, 47% females) diagnosed with autism spectrum disorder (ASD), attention-deficit/hyperactivity disorder (ADHD), other NDDs, or typically developing individuals. We used the Reading the Mind in the Eyes Test to operationalize ToM, the Fragmented Pictures Test for central coherence (CC), the Tower Test for executive functioning (EF), and the general ability index in the Wechsler Intelligence Scales for IQ. In the linear regressions, weak CC and a lower IQ were associated with a reduced ToM ability across pairs. Female sex and higher age were robustly associated with increased ToM ability, whereas EF was not associated with ToM. In the within-pair analyses, where unmeasured familial confounders are implicitly adjusted, the associations between ToM and other cognitive functions, were attenuated and the association with CC was non-significant. The result suggests that familial factors shared by the twins, such as genetic and shared environment, influence the association between CC, IQ, and ToM. Future studies need to include a larger sample of monozygotic twins, who are genetically identical, in order to draw more firm conclusions regarding the influence of familial factors, and to differentiate between shared environmental and genetic effects on the associations between cognitive functions.