As the number of people sickened in an outbreak of Legionnaires’ disease in the South Bronx climbed to 71 on Sunday, health officials were still piecing together where the illness, a form of pneumonia spread through airborne water droplets, might have originated.

Four of the people stricken with Legionnaires’ have died from the disease, which can spread when people breathe in water droplets from rooftop cooling towers, fountains or even showers connected to water systems where legionella bacteria thrive. Five cooling towers in the South Bronx have tested positive for legionella — including towers at the Opera House Hotel and the Lincoln Medical and Mental Health Center — but health investigators have not determined which is responsible for the outbreak.

The outbreak has prompted calls for more regular inspections of cooling towers.

Officials are confident that the disease spread from one or more of the five cooling towers, not from another water source, because interviews with the patients have shown that the only thing those who fell sick had in common was living and working in the same few South Bronx neighborhoods.

Given that, “it would not have been possible for them to all be infected from one Jacuzzi or one shower,” said Dr. Jay Varma, the deputy commissioner for disease control at the New York City Department of Health and Mental Hygiene. “It may take a few weeks for us to do the lab detective work that’s needed to conclusively say whether it was one cooling tower or all five.”