The spreading of fake news or misinformation about COVID-19 on social media is a serious threat to societies and hindering nations of the world in overcoming the pandemic. Most of the conducted research on tackling COVID-19 misinformation by exploiting technology fail to depict the reality of misinformation spreading as only one social media platform is being investigated. This research aims to understand the spreading of COVID-19 misinformation across different social media platforms. To gain these insights, a data set that includes classified COVID-19 misinformation and credible information has been compiled. Each information can be identified on Twitter and Reddit by a unique URL. These URLs were derived from established fact checking corpuses and credible news sources. The URLs were then used as search terms to scrape tweets, submissions, and comments from Twitter and Reddit. The data was analyzed using two different classifier machine learning algorithms. The analysis shows that misinformation moves from one platform to the other faster than credible information. Furthermore, the platform of origin seems to play a minor role in cross-platform spreading patterns. The main contributions of this work are patterns that have been found for cross-platform COVID-19 misinformation spreading.