The production company must indeed inform the police or whichever law enforcement officials are in charge of keeping watch over the location if filming is to be done on the streets. This is still the case if the filmmakers are planning to shoot at other public locations.
The police should also be informed if celebrities are coming to the production set. They can work with the hired security to provide additional crowd control and protection for the crew.
The authorities should be consulted by members of the film crew if there are plans to stage crimes, accidents, and elaborate students. Filmmakers should also inform the police beforehand if firearms and other weapons are going to be used.