We examine transmission scheduling by medium access control (MAC) for energy-efficient detection using Wireless Sensor Networks (WSN). We focus on the binary hypothesis testing problem. The decision is made by an access point and based on received data from sensors that transmit through a fading channel. We study the significance of exploiting both Channel-State Information (CSI) and Likelihood-Ratio Information (LRI) to design adequate MAC protocol that minimizes the total transmission energy required for the detection problem. By formulating the problem as a Stochastic Shortest Path (SSP) problem we design the LRI and CSI Based Access (LCBA) protocol. LCBA trades off between LRI and CSI to minimize the total transmission energy. It allows sensors to access the channel according to the optimal policy which solves the formulated SSP problem.