This paper describes a non-contact breathing detection system using a pyro-electric infrared (PIR) sensor and an accelerometer. The multi-sensor system can be used to detect the respiratory disorders. A PIR sensor is placed onto a stand near a bed and an accelerometer is placed on the mattress. We recently developed a PIR sensor which is capable of producing 1-D time-varying signals corresponding to the motions in its field of view. The PIR sensor signal due to the thoracic movements turns out to be an almost periodic signal. Similarly, the accelerometer produces an almost periodic signal in response to vibrations in bed. Sensor signals are processed using a topological approach. Point clouds are constructed from the delay-coordinate embedding of the time series sensor data first. Then, periodic structures in the point clouds are detected using persistent homology. The sensors, with the proposed method, complement each other to produce more accurate decisions in different lying positions.