Hyperparameter optimization (HPO) aims to identify an optimal hyperparameter configuration (HPC) such that the resulting model generalizes well to unseen data. As the expected generalization error cannot be optimized directly, it is estimated with a resampling strategy, such as holdout or cross-validation. This approach implicitly assumes that minimizing the validation error leads to improved generalization. However, since validation error estimates are inherently stochastic and depend on the resampling strategy, a natural question arises: Can excessive optimization of the validation error lead to overfitting at the HPO level, akin to overfitting in model training based on empirical risk minimization? In this paper, we investigate this phenomenon, which we term overtuning, a form of overfitting specific to HPO. Despite its practical relevance, overtuning has received limited attention in the HPO and AutoML literature. We provide a formal definition of overtuning and distinguish it from related concepts such as meta-overfitting. We then conduct a large-scale reanalysis of HPO benchmark data to assess the prevalence and severity of overtuning. Our results show that overtuning is more common than previously assumed, typically mild but occasionally severe. In approximately 10% of cases, overtuning leads to the selection of a seemingly optimal HPC with worse generalization error than the default or first configuration tried. We further analyze how factors such as performance metric, resampling strategy, dataset size, learning algorithm, and HPO method affect overtuning and discuss mitigation strategies. Our results highlight the need to raise awareness of overtuning, particularly in the small-data regime, indicating that further mitigation strategies should be studied.