Background: Many studies have shown that sociodemographic variables significantly predict the use of complementary and alternative medicine (CAM), although these predictions were not particularly strong. A multitude of predictors of the use or approval of CAM have been investigated in the field of personal values and worldviews, but the effects were small or doubtful due to non-representative samples. More recent psychological research has linked positive attitudes towards CAM with intuitive thinking, paranormal beliefs, ontological confusions and magical health beliefs, suggesting a common thinking style behind all these variables. The aim of this study is to identify the most important predictors of the use and approval of CAM. Methods: We performed a canonical correlation analysis on all 3480 records from the 2012 German General Social Survey (ALLBUS) with the lifetime use and opinion of CAM as the dependent variables. Results: Approval of paranormal practices such as fortune-telling, dowsing or spiritualism explained 32% of the variance in the dependent canonical variate "approval of CAM", while sociodemographic variables explained only 2%. Experience with paranormal practices explained 17% of the variance in the dependent canonical variate "experience with CAM", and sociodemographic variables explained 10% of the variance. Traditional religiosity, attitudes towards science and post-materialist values showed no relevant correlations with the dependent canonical variates. Conclusions: Paranormal beliefs and related measures are the most important known predictors of the use and approval of CAM. Experience with paranormal practices not only indicates paranormal beliefs but also explains experience with CAM that cannot be explained by approval of CAM. Female gender and higher socioeconomic status predict experience with CAM without predicting approval of CAM, but their influence should not be overstated.