Regarding sleep research, polysomnography (PSG) also called a sleep study, is a gold standard. It incorporates brain waves, the oxygen level in the blood, heart rate and breathing, and leg movement recordings. PSG is a complicated and expensive laboratory-based procedure, usually done in hospitals or special sleep center. In this study, an alternative technique for Sleep-Related Breathing Disorders (SRBD) based on selected cardiac and acoustic parameters and the Random Forest (RF) has been studied. A system dedicated to the detection of simultaneously acquired ECG and acoustic signals, which are collected during sleep at home environment is proposed. Results obtained indicate that classification and regression tree models such as RF are appropriate for the evaluation of sleep disorders like SRBD. The best identification of sleep irregularities at level 89.00 percent for the raw database was obtained. Thus, statistical predictive models allow identification of breathing events with high levels of sensitivity and specificity, providing an inexpensive and accurate diagnosis.