Several governments introduced or promoted the use of contact-tracing apps during the ongoing COVID-19 pandemic. In Germany, the related app is called Corona-Warn-App, and by end of 2020, it had 22.8 million downloads. Contact tracing is a promising approach for containing the spread of the novel coronavirus. It is only effective if there is a large user base, which brings new challenges like app users unfamiliar with using smartphones or apps. As Corona-Warn-App is voluntary to use, reaching many users and gaining a positive public perception is crucial for its effectiveness. Based on app reviews and tweets, we are analyzing the public perception of Corona-Warn-App. We collected and analyzed all 78,963 app reviews for the Android and iOS versions from release (June 2020) to beginning of February 2021, as well as all original tweets until February 2021 containing #CoronaWarnApp (43,082). For the reviews, the most common words and n-grams point towards technical issues, but it remains unclear, to what extent this is due to the app itself, the used Exposure Notification Framework, system settings on the user's phone, or the user's misinterpretations of app content. For Twitter data, overall, based on tweet content, frequent hashtags, and interactions with tweets, we conclude that the German Twitter-sphere widely reports adopting the app and promotes its use.