Hi there! It was a very interesting reading, thanks to all who posted. My final take on this subject is that European and US laws look pretty different. I’m neither a lawyer nor a LEO, but this seems rather evident to me. In Italy, but more generally in Europe, LEOs have two areas where their activities are legit, according to current laws.
One area is within the so called Judicial Police activities (kind of CID). Important to note the Judicial Police activities are repressive and not preventive, because it intervenes when a violation has already occurred. Basically, when operating within this area, every LEO has the mandate and the right to e.g.: take notice of the crimes and work in search of information, also on their own initiative entirely. Until the Public Prosecutor takes over the direction of the investigations, the Judicial Police must continue their activities with the sole obligation to keep the Public Prosecutor informed. They seek out for the perpetrators, collect evidences (through intelligence, targeted searches of people, vehicles, houses and premises, seizures of assets/capitals, photographic surveys, etc.). Judicial police activity must be exercised starting from the very acknowledgment of a crime offense and must also be activated before receiving orders from the Public Prosecutor's Office. In our case, if LEOs are working within this area and they question me, I am already a "suspect" for them and they are obliged to notify me this. If I am in the clear, I think it’s still good to be honest and transparent, so they can tick me off their list and go ahead with their investigations. Sure, if I am not in the clear or the going gets tough, it’s probably a good advice to keep mouth shut and look for a good lawyer.
Second area is the so called Public Security. Officials and public security officers monitor the maintenance of public order, they safeguard the safety and protection of people and their properties, work to prevent offenses/crimes, collect evidence of these and arrest the perpetrators before or during the happening; they survey compliance to the laws and also assist in case of public and private disputes, accidents/incidents, etc. Note the big difference here is the crimes have still to happen or just happening, all these activities are kind of preventive or containment actions, so to say. In our case, if LEOs are working within this area and question me I am not a suspect, just a Citizen. They don't need to notify me anything, it's their right and duty to stop me, question me, ask me to identify myself and even search me on spot. I can become a "suspect" entirely based on my behavior and their findings, though. So, if I am in the clear with nothing to hide and totally aligned with legislation prescriptions, I still think it would be much better for me to answer, tell the truth straight away, show my papers, ID, thank them for their service and walk away. Also note that, while it would be surely my “right” to refuse saying anything, not showing ID, etc. this rarely ends up well. The best I can hope for is to spend three/four hours in the Police Station and have a “forced” identification. Since the officers had to do extra job for this, normally they start searching for other things and it’s not uncommon they would issue a search warrant, just to be sure I'm not a terrorist, drug dealer, etc. So from a small thing, it can soon become a huge hassle. Gun/hunting permit also – if someone has one - can be put on hold, just for the generic “hindrance to the investigation” cause, etc.
So I believe it’s still good to be aware of own specific legislations and laws, our rights and our duties. Normally, from my experience, it’s also very much about how we relate with LEOs and authorities in general. It would be very interesting for me if a real LEO/Policeman could chime in here and say something about this. Take care and stay safe!