The worldwide COVID-19 pandemic puts countries and their governments in an unprecedented situation. Strong countermeasures have been implemented in most places, but how much do people trust their governments in handling this crisis? Using data from a worldwide survey, conducted between March 20th and April 22nd, 2020, with more than 100,000 participants, we study people's perceptions of government reactions in 57 countries. We find that media freedom reduces government trust directly as well as indirectly via a more negative assessment of government reactions as either insufficient or too strict. Higher level of education is associated with higher government trust and lower tendency to judge government reactions as too extreme. We also find different predictors of perceived insufficient reactions vs. too-extreme reactions. In particular, number of COVID-19 deaths significantly predicts perceived insufficient reactions but is not related to perceived too-extreme reactions. Further survey evidence suggests that conspiracy theory believers tend to perceive government countermeasures as too strict.