Brain activations underlying control of breathing are not completely known. Furthermore, the coupling between neural and respiratory dynamics is usually estimated through linear correlation measures, thus totally disregarding possible underlying nonlinear interactions. To overcome these limitations, in this preliminary study we propose a nonlinear coupling analysis of simultaneous recordings of electroencephalographic (EEG) and respiratory signals at rest and after variation of carbon dioxide (CO2) level. Specifically, a CO2 increase was induced by a voluntary breath hold task. EEG global field power (GFP) in different frequency bands and end-tidal CO2 (PETCO2) were estimated in both conditions. The maximum information coefficient (MIC) and MIC-ρ2 (where ρ represents the Pearson's correlation coefficient) between the two signals were calculated to identify generic associations (i.e. linear and nonlinear correlations) and nonlinear correlations, respectively. With respect to a free breathing state, our results suggest that a breath hold state is characterized by an increased coupling between respiration activity and specific EEG oscillations, mainly involving linear and nonlinear interactions in the delta band (1-4 Hz), and prevalent nonlinear interactions in the alpha band (8-13 Hz).