Relay network is proposed as a means of improving the error performance and energy efficiency of the wireless networks. Inspired by the battery power efficiency (BPE) analysis in , relay selection from the battery energy efficiency perspective turns out to be an interesting topic. Under the general network setup which integrates typical transmission and reception modules, we adopt the realistic nonlinear battery model, extend the BPE results in  to relay network over Rayleigh fading channels, investigate the optimum and suboptimum energy allocation solutions for the relaying transmission, and finally establish the relay selection criterion from the battery energy efficiency point of view. Both the theoretical derivation and numerical results show that, subject to the same average bit error rate (BER) performance constraint, relaying does not necessarily increase the system energy efficiency, but is a possible alternative of the direct transmission depending on the relaying situation. Additionally, we prove that the two relaying protocols Decode and Forward (DF) and Amplify and Forward (AF) are equivalent for relay selection over Rayleigh fading channels at high SNR.