Italy has a difficult system to understand when it comes to emergency services.
This will try and break it down with details of who to contact.
I think the simple rule of thumb is unlike most countries where you dial one number ie 911, 999 or 112, its easier to phone direct to the service you require.
Italy has a number of different police forces, including your local one controlled by the local council (commune) A regional one then you have the military type (Carabinieri) You will find for emergencies people normally go straight to the Carabinieri rather than one of the police forces. And in general that is probably the best advice, the local police tend to man events rather than deal with crimes. Now I'm sure officially they say differently, but in practice that is how it works.
112 is the number for Carabinieri in Italy. In many areas 112 or 999 actually go through to them as well.
113 is also a number classed as emergency police help, which you can use to ask for emergency help.
Ambulances and Medical Emergencies
Depending on the area depends on the ambulance service, in many parts of italy including most towns and villages, Ambulances are manned by volunteers rather than the local health authority. In big cities its nearly always managed by the local health service.
If you have a medical health emergency out of hours you phone the regional control centre on 118. During working hours you go to a doctor rather than phone the emergency helpline.
118 is the number for Ambulances and Medical Emergencies
In Italy pharmacies can deal with many things, including the dispensing of many prescription drugs without the need to go to a doctor, so sometimes its actually quicker and easier to go to a pharmacy, many areas have 24 hour ones or they have ones open on rotation, so you will find a pharmacy open all year round.
Nearly every town and city has emergency doctors out of hours, the commune (local council) arranged them, normally found near the police station or the actual commune building, but the number is widely advertised or 118 can direct you to them.
Italy has a national number for the fire service which is 115. However this is where it gets confusing, if its a forest fire then its 1515