Obstructive sleep apnea (OSA) is a common sleep disorder that causes increasing risk of mortality and affects quality of life of approximately 6.62% of the total US population. Timely detection of sleep apnea events is vital for the treatment of OSA. In this paper, we present a novel approach based on extracting the quantifiers of nonlinear dynamic cardio-respiratory coupling from electrocardiogram (ECG) signals to detect sleep apnea events. The quantifiers of the cardio-respiratory dynamic coupling were extracted based on recurrence quantification analysis (RQA), and a battery of statistical data mining techniques were to enhance OSA detection accuracy. This approach would lead to a cost-effective and convenient means for screening of OSA, compared to traditional polysomnography (PSG) methods. The results of tests conducted using data from PhysioNets Sleep Apnea database suggest excellent quality of the OSA detection based on a thorough comparison of multiple models, using model selection criteria of validation data: Sensitivity (91.93%), Specificity (85.84%), Misclassification (11.94%) and Lift (2.7).