We　propose　a　data-driven　least-square　cross-validation　method　to　optimally　select　smoothing　parameters　for　the　nonparametric　estimation　of　conditional　cumulative　distribution　functions　and　conditional　quantile　functions.　We　allow　for　general　multivariate　covariates　that　can　be　continuous,　categorical,　or　a　mix　of　either.　We　provide　asymptotic　analysis,　examine　finite-sample　properties　via　Monte　Carlo　simulation,　and　consider　an　application　involving　testing　for　first-order　stochastic　dominance　of　children＇s　health　conditional　on　parental　education　and　income.　This　article　has　supplementary　materials　online.