Research works on operator monitoring underline the benefit of taking into consideration several signal modalities to improve accuracy for an objective mental state diagnosis. Heart rate (HR) is one of the most utilized systemic measures to assess cognitive workload (CW), whereas, respiration parameters are hardly utilized. This study aims at verifying the contribution of analyzing respiratory signals to extract features to evaluate driver's activity and CW variations in driving. Eighteen subjects participated in the study. The participants carried out two different cognitive tasks requiring different CW demands, a single task as well as a competing cognitive task realized while driving in a simulator. Our results confirm that both HR and breathing rate (BR) increase in driving and are sensitive to CW. However, HR and BR are differently modulated by the CW variations in driving. Specifically, HR is affected by both driving activity and CW, whereas, BR is suitable to evidence a variation of CW only when driving is not required. On the other hand, spectral features characterizing respiratory signal could be also used similarly to HR variability indices to detect high CW episodes. These results hint the use of respiration as an alternative to HR to monitor the driver mental state in autonomic vehicles in order to predict the available cognitive resources if the user has to take over the vehicle.