Test case design is the key to effective quality inspection of electrical equipment. To tackle the challenges of inadequate scenario coverage and disparate difficulty levels in the detection of single-phase ground faults in power distribution primary and secondary fusion switch, we propose a case construction method utilizing Latin hypercube sampling (LHS) based on NSGA-II double-objective optimization. Initially, the method investigates the primary factors influencing waveform detection difficulty and determines their respective weights through measurement and calculation, thus establishing a comprehensive model for calculating difficulty coefficients. Then, based on the dual objectives of uniformity and difficulty balance, we introduce a double-objective optimization LHS generation algorithm to construct a multi-dimensional detection cases of single-phase ground fault in power distribution primary and secondary fusion switch. Finally, the difficulty coefficient calculation model and the constructed test case undergo validation using actual test results, demonstrating a 43.59% efficiency improvement on the premise of ensuring the detection efficacy.