We provide the first broad-scale evidence regarding the effect of school reopenings on COVID-19 health outcomes. We specifically focus on COVID-19-related hospitalizations, which directly measure the health outcomes of greatest interest and are not subject to the numerous measurement problems that arise with virus positivity rates and contact tracing. We also address selection bias in school reopening decisions by using panel analysis of weekly school reopening and COVID-19 hospitalization data for almost every county in the nation. In addition to fixed effects and matched difference-in-differences methods, we use teacher bargaining power as an instrumental variable. For counties whose pre-opening total new COVID-19 hospitalization rates were below roughly 36-44 per 100,000 population per week (roughly the 75th percentile of counties during the summer), we find no effect of in-person school reopening on COVID-19 hospitalization rates. For these counties, the estimates are robust to alternative school reopening and hospitalization data sources, the addition of controls for general state social distancing policies and college opening modes, and alternative estimation methods. For counties where total baseline new hospitalizations are above the 36-44 new hospitalizations per 100,000 per week, the estimates are inconsistent across methods and are therefore inconclusive. Our work contributes to the ongoing debate on teaching modes during the COVID-19 pandemic and the costs and benefits of remote education.