Do countries with differing political institutions respond differently to a national crisis? The coronavirus pandemic, where almost all countries were hit by the same crisis in a short span of time, provides a rare opportunity to answer this question. For a sample of 125 countries, we use high frequency data on two measures of policy response- (i) containment policies, relating to closure of public spaces and restrictions on movement of people, and (ii) health policies, relating to public information campaigns, testing and contact tracing, to examine their policy response to the crisis. We show that: first, non-democracies have more stringent containment and health policies prior to their first COVID-19 case. However, after registering their first case, democracies either close this gap (in containment policies), or surpass non-democracies (in health policies) within a week. Second, policy responses do not differ by governance systems (presidential or parliamentary) in democracies. However, elected leaders who performed better in the last election or face their next election farther in the future are more aggressive in their policy response. Third, democracies with greater media freedom respond more slowly in containment policies, but are more aggressive in health policies. Lastly, more conducive political norms (such as trust in the elected government) systematically predict a more aggressive response in both containment and health policies. Our analysis therefore suggests that political institutions and the incentives of the political leaders embedded therein, significantly shape the policy response of governments to a national crisis.