Causality analysis of simultaneous measurements of the brain's electrical activity and its hemodynamic activity provides the opportunity to study the neural underpinning of hemodynamic fluctuations. This multimodal analysis can also be used to extract valuable information regarding the location of the generators of various electrical events such as Alpha rhythms or epileptiform activity. To best of our knowledge, we are the first propose a method to assess causality from EEG to the hemodynamic activity measured using functional near-infrared spectroscopy (fNIRs). The main challenge in studying causality within this setting arises from the low sampling rate of the fNIRs and the mixed frequency nature of the data. Our method of analysis consists of two parts. Through a simple modification of Geweke's formulation of contamination, we first show that the low sampling frequency of the fNIRs does not cause contamination in estimating causality from EEG to fNIRs. We then apply a novel causality test to avoid the down-sampling of the EEG when measuring for causality. The method of analysis proposed here can be generalized to study causality in other biomedical signal analysis applications and mixed frequency settings.