This paper examines the validity of using the bootstrap for inference in matching estimators, which are widely used to evaluate programs or treatments. The authors show that the bootstrap is generally not valid, even in simple cases with a single continuous covariate when the estimator is root-$N$ consistent and asymptotically normally distributed with zero asymptotic bias. Due to the extreme non-smoothness of nearest neighbor matching, the standard conditions for the bootstrap are not met, leading to diverging bootstrap variances from the actual variance. Simulations confirm the difference between actual and nominal coverage rates for bootstrap confidence intervals, as predicted by theoretical calculations. This is the first example of a root-$N$ consistent and asymptotically normal estimator where the bootstrap fails to deliver valid confidence intervals. The paper also discusses alternative variance estimators proposed by Abadie and Imbens, which are formally justified under certain conditions.This paper examines the validity of using the bootstrap for inference in matching estimators, which are widely used to evaluate programs or treatments. The authors show that the bootstrap is generally not valid, even in simple cases with a single continuous covariate when the estimator is root-$N$ consistent and asymptotically normally distributed with zero asymptotic bias. Due to the extreme non-smoothness of nearest neighbor matching, the standard conditions for the bootstrap are not met, leading to diverging bootstrap variances from the actual variance. Simulations confirm the difference between actual and nominal coverage rates for bootstrap confidence intervals, as predicted by theoretical calculations. This is the first example of a root-$N$ consistent and asymptotically normal estimator where the bootstrap fails to deliver valid confidence intervals. The paper also discusses alternative variance estimators proposed by Abadie and Imbens, which are formally justified under certain conditions.