This paper investigates the pattern of COVID-19 contagion in Portuguese municipalities from March 23rd to April 5th (the exponential phase). We have recurred to spatial autocorrelation models to discuss how the conglomeration of highly infectious spaces has also contributed to infecting neighbouring municipalities. We have used several indicators for the contagion of COVID-19 from the number of infectious individuals to rates of infectious. As explicative variables, additionally to spatial proximity, we also considered population density, the share of the elderly population as well as the length of municipal perimeter/border. Our results show that highly dense municipalities tended to contaminate close areas. Lengthier perimeters also showed a positive effect on the contagious indicators for a given municipality.