Type III sleep studies record cardio-respiratory channels only. Compared with polysomnography, which also records electrophysiological channels, they present many advantages: they are less expensive, less time-consuming, and more likely to be performed at home. However, their accuracy is limited by missing sleep information. That is why many studies present specific cardio-respiratory parameters to assess the causal effects of sleep stages upon cardiac or respiratory activities. For this paper, we gathered many parameters proposed in literature, leading to 1,111 features. The pulse oximeter, the PneaVoX sensor (recording tracheal sounds), respiratory inductance plethysmography belts, the nasal cannula and the actimeter provided the 112 worthiest ones for automatic sleep scoring. Then, a 3-step model was implemented: classification with a multi-layer perceptron, sleep transition rules corrections (from the AASM guidelines), and sequence corrections using a Viterbi hidden Markov model. The whole process was trained and tested using 300 and 100 independent recordings provided from patients suspected of having sleep breathing disorders. Results indicated that the system achieves substantial agreement with manual scoring for classifications into 2 stages (wake vs. sleep: mean Cohen's Kappa κ of 0.63 and accuracy rate Acc of 87.8%) and 3 stages (wake vs. R stage vs. NREM stage: mean κ of 0.60 and Acc of 78.5%). It indicates that the method could provide information to help specialists while diagnosing sleep. The presented model had promising results and may enhance clinical diagnosis.