The World Health Organization has not only signaled the health risks of COVID-19, but also labeled the situation as infodemic, due to the amount of information, true and false, circulating around this topic. Research shows that, in social media, falsehood is shared far more than evidence-based information. However, there is less research analyzing the circulation of false and evidence-based information during health emergencies. Thus, the present study aims at shedding new light on the type of tweets that circulated on Twitter around the COVID-19 outbreak for two days, in order to analyze how false and true information was shared. To that end, 1000 tweets have been analyzed. Results show that false information is tweeted more but retweeted less than science-based evidence or fact-checking tweets, while science-based evidence and fact-checking tweets capture more engagement than mere facts. These findings bring relevant insights to inform public health policies.