Sleep is extremely important for physical and mental health. Although polysomnography is an established approach in sleep analysis, it is quite intrusive and expensive. Consequently, developing a non-invasive and non-intrusive home sleep monitoring system with minimal influence on patients, that can reliably and accurately measure cardiorespiratory parameters, is of great interest. The aim of this study is to validate a non-invasive and unobtrusive cardiorespiratory parameter monitoring system based on an accelerometer sensor. This system includes a special holder to install the system under the bed mattress. The additional aim is to determine the optimum relative system position (in relation to the subject) at which the most accurate and precise values of measured parameters could be achieved. The data were collected from 23 subjects (13 males and 10 females). The obtained ballistocardiogram signal was sequentially processed using a sixth-order Butterworth bandpass filter and a moving average filter. As a result, an average error (compared to reference values) of 2.24 beats per minute for heart rate and 1.52 breaths per minute for respiratory rate was achieved, regardless of the subject’s sleep position. For males and females, the errors were 2.28 bpm and 2.19 bpm for heart rate and 1.41 rpm and 1.30 rpm for respiratory rate. We determined that placing the sensor and system at chest level is the preferred configuration for cardiorespiratory measurement. Further studies of the system’s performance in larger groups of subjects are required, despite the promising results of the current tests in healthy subjects.