Even in America, I can't imagine someone suing the city because they got injured during a storm, let alone winning their case and making the city pay.
The real story was someone got killed by lighting, and the city decided to "do something" so that never happened again. However, IMHO, they're going to shoot themselves in the foot because their citizens are going to be less papered for a tornado, which could kill many more people.
In Germany, you absolutely can. It's called "Verkehrssicherungspflicht". Given how Americans can get sued by a random child wandering onto their property and injuring themselves on a trampoline or a swimming pool, even if the area is fenced off, I assumed that liability for natural disasters would be just as insane.
It's definitely city-level, in at least some places. I know because I was visiting a friend and heard the sirens go off. I assumed it was a tornado warning (i.e. actually serious), but it turns out that city (and only that city in the area) is dumb and blare the sirens for severe thunderstorm warnings, basically crying wolf every time.