The repeated reuse of test sets in popular benchmark problems raises doubts about the credibility of reported test error rates. Verifying whether a learned model is overfitted to a test set is challenging as independent test sets drawn from the same data distribution are usually unavailable, while other test sets may introduce a distribution shift. We propose a new hypothesis test that uses only the original test data to detect overfitting. It utilizes a new unbiased error estimate that is based on adversarial examples generated from the test data and importance weighting. Overfitting is detected if this error estimate is sufficiently different from the original test error rate. The power of the method is illustrated using Monte Carlo simulations on a synthetic problem. We develop a specialized variant of our dependence detector for multiclass image classification, and apply it to testing overfitting of recent models to two popular real-world image classification benchmarks. In the case of ImageNet, our method was not able to detect overfitting to the test set for a state-of-the-art classifier, while on CIFAR-10 we found strong evidence of overfitting for the two recent model architectures we considered, and weak evidence of overfitting on the level of individual training runs.