In randomized clinical trials, it is standard to include baseline variables in the primary analysis as covariates, as it is recommended by international guidelines. For the study design to be consistent with the analysis, these variables should also be taken into account when calculating the sample size to appropriately power the trial. Because assumptions made in the sample size calculation are always subject to some degree of uncertainty, a blinded sample size reestimation (BSSR) is recommended to adjust the sample size when necessary. In this article, we introduce a BSSR approach for count data outcomes with baseline covariates. Count outcomes are common in clinical trials and examples include the number of exacerbations in asthma and chronic obstructive pulmonary disease, relapses, and scan lesions in multiple sclerosis and seizures in epilepsy. The introduced methods are based on Wald and likelihood ratio test statistics. The approaches are illustrated by a clinical trial in epilepsy. The BSSR procedures proposed are compared in a Monte Carlo simulation study and shown to yield power values close to the target while not inflating the type I error rate.