Not true! In many countries there are multiple forces...
"Law enforcement in Italy is centralized on a national level, carried out by multiple national forces, helped by few limited local agencies."
(Wikipedia, Law enforcement in Italy)
In Italy that's not for competition though: it is to prevent that a single ministry has too much power by denying them full control of law enforcement.
The Police answers to the Ministry of the Interior whereas the Carabinieri are a branch of the Army and answer to the Ministry of Defense.