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High computational complexity and difficulty in taking an analytical expression of detection statistics are some of the problems encountered when using the statistical resolution limit (SRL) analysis in the generalized likelihood ratio test (GLRT). A Rao test-based method is used in this paper to analyze the 1-D SRL of two closely spaced signals, which can simplify the derivation of detection statistics, reduce the computational complexity, and improve the detection performance in some scenarios. In the proposed approach, two cases are considered based on the interference sources that are either involved or not in the received signals. Moreover, in each case, the detection statistic is derived by assuming the known or unknown variance of the added noise, respectively. For the performance comparison, the GLRT detection statistic is also identified. The relationship between the SRL and the required minimum signal-to-noise ratio/signal-to-interference-plus-noise ratio is also obtained to resolve the two adjacent signal sources. Then, the detection performance and computational complexity are evaluated. The simulation results are used to verify the effectiveness and superiority of the Rao test.