Background: Death certificates are considered the most reliable source of information to compare cause-specific mortality across countries. The aim of the present study was to examine death certificates of persons who tested positive for severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) to (a) quantify the number of deaths directly caused by coronavirus 2019 (COVID-19); (b) estimate the most common complications leading to death; and (c) identify the most common comorbidities. Methods: Death certificates of persons who tested positive for SARS-CoV-2 provided to the National Surveillance system were coded according to the 10th edition of the International Classification of Diseases. Deaths due to COVID-19 were defined as those in which COVID-19 was the underlying cause of death. Complications were defined as those conditions reported as originating from COVID-19, and comorbidities were conditions independent of COVID-19. Results: A total of 5311 death certificates of persons dying in March through May 2020 were analysed (16.7% of total deaths). COVID-19 was the underlying cause of death in 88% of cases. Pneumonia and respiratory failure were the most common complications, being identified in 78% and 54% of certificates, respectively. Other complications, including shock, respiratory distress and pulmonary oedema, and heart complications demonstrated a low prevalence, but they were more commonly observed in the 30–59 years age group. Comorbidities were reported in 72% of certificates, with little variation by age and gender. The most common comorbidities were hypertensive heart disease, diabetes, ischaemic heart disease, and neoplasms. Neoplasms and obesity were the main comorbidities among younger people. Discussion: In most persons dying after testing positive for SARS-CoV-2, COVID-19 was the cause directly leading to death. In a large proportion of death certificates, no comorbidities were reported, suggesting that this condition can be fatal in healthy persons. Respiratory complications were common, but non-respiratory complications were also observed.