I would add that 911 is a "queer" choice (for rotary phones), in other countries the emergency numbers are lowish numbers, in Italy 112 or 113 (or 115), and there are several records in the past of people managing to "dial" them by quickly pushing and releasing the hook switch.
There was another reason for this as it was common, many, many years ago, to restrict the possibility to make phone calls by using a little lock on the dial, like this:
Did you introduce the EU emergency number as the national one? If so - good choice.
In France we have the plethora of numbers (15, 17, 18 - I actually do not know what 16 does), and also 112.
We are still teaching "18" as the primary number (you get the firemen who will either come for a fire, or for an accident, or dispatch). We could go for 112 (and keep the older number for a generation, redirecting them to 112) and not rely on people to know which number to call.
UPDATE: I just asked my 17 yo son which number he would call in an emergency and he said 112. So there is hope :)
JFYI, besides and before the EU emergency number, in Italy we traditionally had:
112 Carabinieri (one of the two national "police" corps)
113 Polizia (the other national police corps)
115 Pompieri (Fire Brigade)
118 Ambulanza (Ambulance)
In Italian it is a common phrase "roba da chiamare il 112" o "roba da chiamare il 113" (something that needs a call to 112 or 113) as a synonym of "a serious emergency" and of course if you called those numbers they would anyway forward the call to the appropriate service (like ambulance, fire brigade, etc.).
The EU emergency number is slowly being introduced (some regions have it already, some not yet), but the 112 is already well in the minds of anyone.
> How does/did a citizen make the decision of which police force to call?
It is a good question.
It depends.
There may be territorial choices or also "political" ones.
Typically Carabinieri have more presence in the country/villages/small towns whilst Police have more presence in larger cities (but there are Carabinieri there as well and - additionally - the local police, which were once called Vigili Urbani and now are called Polizia Municipale, and there is also the Polizia Regionale, to the joy of foreigners that do have a really hard time to understand the subtleties), highways and main roads are typically Police only (Polizia Stradale), but minor roads are usually patroled by the Carabinieri.
So usually you call (called) 112 or 113 depending on where you are (where the emergency happens).
The "political" part is even more subtle.
The Carabinieri are a branch of the military, whilst the Police are "civil", people leaning to the right tend to trust the Carabinieri (whose motto is "nei secoli fedele" i.e. "faithful in centuries") more than Police, whilst people leaning to the left tend to trust the Police as being more independent.
Until not so many years ago if you (or your family) had some relationship/contacts with some (left side) parties or association you would have not been allowed to join the Carabinieri (whether this was official policy or simply what happened is another thing).
The popular perception was (is) that the Carabinieri operate strictly by the Law, whilst Police is a little more "giving/flexible" (on minor things).
On the other hand, once it was easier to join the Carabinieri with a lower level of school/education than to join the Police, so we have here all the jokes about stupidity/ignorance targeting the Carabinieri (the same ones that traditionally in the UK are about the Irish or the Polish).
In France we also have two "police" forces: the "gendarmerie" and the "police nationale".
You may know "gendarmerie" from the Louis de Funes movies (Le gendarme de St Tropez, ...) - this is a military unit that mostly works in the countryside.
The "police nationale" is an entity attached to the ministry of interior and does more or less the same things, but more in the cities.
There is a history of hatred between these organizations - yes, this is how stupid we are. They share competencies (the most well known being the elite units - GIGN and RAID)
When you want to call the police, you dial 17 and you get the right one, depending on where you are.
If you have a health problem, you call the 18 (firemen), or the 15 (ambulance).
If there is a fire, you call the 18.
This is why having a single 112 number is easier to teach to children and tourists.
TL;DR Running out of numbers and putting in temporary measures requiring the 16 as prefix. Measures that likely didn't scale as well as expected since we moved on to a different system within basically 10 years.
There was another reason for this as it was common, many, many years ago, to restrict the possibility to make phone calls by using a little lock on the dial, like this:
https://www.ebay.it/itm/402554995319?hash=item5dba25c277:g:~...
it was placed on the #3 hole, so that you could dial 112 or 113 even when the lock was on.