This paper shows that the UMP or UMPU tests for serial correlation, derived under the assumption of a normal distribution, are quite robust against departure from normality. In fact, the tests are still UMP or UMPU in much broader classes of distributions and the null distributions remain unchanged under these classes. The results will be applied to a linear model.
"A Robustness Property of the Tests for Serial Correlation." Ann. Statist. 5 (6) 1212 - 1220, November, 1977. https://doi.org/10.1214/aos/1176344005