Monitoring vital signs using microwave signals has significant applications in biology, and also for finding survivors under debris during natural hazards. The vital signs detection radar sensor system consists of a transmitter and a receiver. This system can be considered as a wireless system. In the wireless system, the outage probability is a crucial factor to evaluate the reliability of the system. This work investigates the outage probability (OP) of a radar sensor system under the Nakagami-m environment. The dependence of the OP on different parameters like operating frequency, distance to the measured object, transmitter power, and the leakage between transmitter and receiver antennae is examined. The theoretical model for the OP is validated with simulation results through various environments.