A generalized bootstrap version is defined for degenerate $U$-statistics. Our main result shows that the (conditional) distribution function of the bootstrapped degenerate $U$-statistic provides a consistent estimator for the unknown distribution function of the degenerate $U$-statistic under consideration. For the proof we rely on a rank statistic approach.
"Consistency of the Generalized Bootstrap for Degenerate $U$-Statistics." Ann. Statist. 21 (4) 1811 - 1823, December, 1993. https://doi.org/10.1214/aos/1176349399