It has been suggested that the right hemisphere lateralization typically observed for face processing may depend on lateralization of written word processing to the left hemisphere; a pattern referred to as the causal complementary principle of lateralization. According to a strong version of this principle, a correlation should be found between the degree of left and right hemisphere lateralization for word and face processing respectively. This has been observed in two studies, but only for left-handed individuals. The present study tested whether a similar lateralization pattern could be found in a relatively large sample of right-handed individuals (N = 210) using behavioral measures (divided visual field paradigms). It was also tested whether the degree of right hemisphere lateralization for face and global shape processing would correlate positively, as predicted by a strong version of the input asymmetry principle of lateralization. This was tested in a subsample (n = 189). Bayesian analyses found no evidence for lateralization interdependency as the observed data were 4–17 times more likely under the null hypothesis. Unfortunately, the reliabilities of the lateralization measures were found to be poor. While this dampens the firmness of the conclusions that can be drawn, it is argued that at present there is no positive evidence for strong interdependency between written word and face processing in right-handed individuals.