In a clinical trial to compare two treatments, suppose that patients are assigned to treatment according to a certain class of restricted randomization rules. Conditional on the difference in numbers between the two treatment groups, the asymptotic null distribution of a class of permutation tests is shown to be Gaussian.
"Conditional Inference for Restricted Randomization Designs." Ann. Statist. 16 (3) 1155 - 1161, September, 1988. https://doi.org/10.1214/aos/1176350952