In this work we employ a nonlinear data analysis method called recurrence quantification analysis (RQA) to analyze differences between sleep stages and wake using cardio-respiratory signals, only. The data were recorded during full-night polysomnographies of 313 healthy subjects in nine different sleep laboratories. The raw signals are first normalized to common time bases and ranges. Thirteen different RQA and cross-RQA features derived from ECG, respiratory effort, heart rate and their combinations are additionally reconditioned with windowed standard deviation filters and ZSCORE normalization procedures leading to a total feature count of 195. The discriminative power between Wake, NREM and REM of each feature is evaluated using the Cohen's kappa coefficient. Besides kappa performance, sensitivity, specificity, accuracy and inter-correlations of the best 20 features with high discriminative power is also analyzed. The best kappa values for each class versus the other classes are 0.24, 0.12 and 0.31 for NREM, REM and Wake, respectively. Significance is tested with ANOVA F-test (mostly p <0.001). The results are compared to known cardio-respiratory features for sleep analysis. We conclude that many RQA features are suited to discriminate between Wake and Sleep, whereas the differentiation between REM and the other classes remains in the midrange.