Device to device (D2D) communications enable mobile devices to directly communicate with each other when they are relatively close to each other. We consider the selection of direct or indirect communication path via the base station for D2D communications. Referring to this as the mode selection problem, in this paper we define mode selection rules based on channel capacity, SNR and distance. We also define associated performance metrics by modeling the mode selection problem as a hypothesis test with Gaussian distribution. Furthermore we provide the analytical expressions for correct detection, false alarm, and missed detection probabilities. Our results of the proposed framework can provide sufficient insight about the expected performances through the used mode selection rule for D2D communications.