Does the organisation of healthcare systems affect health outcomes in a pandemic situation? To answer this question, we analysed the effects of the Covid-19 pandemic by focusing on mortality rate outcomes and exploited the heterogeneity of the healthcare organisational models among Italian regions, which makes Italy an ideal "laboratory". Within a common national healthcare system, Italian regions are allowed large autonomy to organise themselves as mixed-markets based on choice and competition, network or centralised leadership models, each delivering different responses to the Covid-19 emergency. Exploiting the discontinuity of healthcare organisational models across the Italian regional borders around Lombardy — the region that most convincingly embraced the mixed-market model fostering competition among health service providers — we applied a difference in geographic regression discontinuity design (DiD-GRDD) to compare mortality rates in 2020 of Lombardy's municipalities with that of neighbouring municipalities in other regions and also exploited the pre-crisis period (2017-2019). Our analysis shows that mortality rates in Lombardy during the first wave were higher by 1-2 percentage points among the population of residents aged 80 years or more, compared to the past, as opposed to regions adopting different organisational models. The mortality rate differential disappeared during the second wave following the implementation of a national policy based on risk zones, limiting mobility and taking stock of the experience developed during the first wave. Finally, by investigating the channels causing higher mortality during the first wave, we show that the role of organisational model differences vanishes, as differential mortality is mostly explained by the decision of the Lombardy regional government to use care homes for hosting Covid-19 patients and reduce the excess demand on the hospital system.