In this paper, we discuss the possibility of performing a sleep evaluation from signals, which are not usually used for this purpose. In particular, we take into consideration the heart rate variability (HRV) and respiratory signals for automatic sleep staging, arousals detection, and apnea recognition. This is particularly useful for wearable or textile devices that could be employed for home monitoring of sleep. The HRV and the respiration were analyzed in the frequency domain, and the statistics on the spectral and cross-spectral parameters put into evidence the possibility of a sleep evaluation on their basis. Comparison with traditional polysomnography (PSG) revealed a classification accuracy of 89.9% in rapid eye movement (REM) non-REM sleep separation and an accuracy of 88% for sleep apnea detection. Additional information can be achieved from the number of microarousals recognized in correspondence of typical modifications in the HRV signal. The obtained results support the idea of automatic sleep evaluation and monitoring through signals that are not traditionally used in clinical PSG, but can be easily recorded at home through wearable devices (for example, a sensorized T-shirt) or systems integrated into the environment (a sensorized bed). This is a first step for the development of systems for sleep screening on large populations that can constitute a complement for the traditional clinical evaluation.