Fusion is widely used to improve the overall detection performance in applications such as radar, wireless sensor networks, wireless communications, spectrum sensing and so on. While the optimum fusion strategy for any preset local decision performance can be easily obtained by the Neyman-Pearson lemma, the selection of the local detection strategy that optimizes the global performance is intractable due to its complexity and the limited global information at local detectors. In this paper, we use large deviation analysis to determine a local decision rule to optimize the asymptotic global performance. Some interesting properties of the decision rule are observed. Numerical results show that our proposed strategy approximates the optimal performance very well even with a small number of local detectors.