This paper considers the test on whether the underlying distribution of an independent and identically distributed sample is a specific member of parametric distribution family. A functional of the difference between the empirical distribution of the sample and estimated parametric distribution can be used as the test statistic but its critical value may be difficult to obtain because the limiting distribution of the test statistic may contain unknown parameters. Bootstrap can be used to estimate the critical value and it was shown by \textit{G.J. Babu} and \textit{C.R. Rao} [Sankhyā 66, No. 1, 63--74 (2004; Zbl 1192.62126)] that the parametric bootstrap, which resamples from the estimated parametric distribution, is consistent but the nonparametric bootstrap, which resamples directly from the empirical distribution of the sample, is not consistent. Babu and Rao also showed that a bias correction to the nonparametric bootstrap test statistic could make it consistent. This paper further establishes, under a series of conditions, the weak approximation for the bias-correct nonparametric bootstrap test statistic. Conditions are verified in the cases where the parametric distribution family is Poisson or normal. Simulations are used to compare the power between the bias-correct nonparametric bootstrap test and parametric bootstrap test.