I always understood it to mean that a policeman has to announce his presence so as to be legit. Like if he knocks on the door and says pizza man, which if said fast enough can sound like policeman, then the arrest or the entry is illegal.
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Maybe. The only general requirement for that entry to be lawful is a warrant. Almost never will a warrantless entry be lawful, and on the rare occasions when it is, an announcement is stupid because there is an apparent life threatening emergency that simply will not allow for delay.
A police officer also does not have to announce the intent to use force (the lawful ability to direct an action carries with it the authority compel compliance without further conversation), with the limited exception of "a warning, if feasible" prior to using deadly force on a dangerous fleeing felon. (The
Garner case fact pattern.) Agencies train it not because it is a good practice (it often is not, tactically) or legally required (it is not, as pointed out), but for political reasons. The staggering ignorance of the law and tactics of force utilization throughout most of the general population, and much to my horror and shame, the vast majority of LE command officers, leads to the development of practices that are not wise, let alone required by law. They exist solely as theater to placate the whiners who think there is some fairness requirement or some such. Hot tip: A uniformed cop with a firearm in the hand is all the warning you should expect. If one does not have a visible weapon, other than personal weapons (hands/feet), the idea of the verbal commands is to reduce the odds of them being stupid and doing something that is or looks like a draw. If they have started the drawing motion, it may already be too late, and it sure as heck is not time to be talking. It's time to move and shoot.
Only once can I recall a temptation to get involved as a private citizen. I walking the dogs last spring when I saw an officer make an obvious Terry stop (contact a suspicious person). I was walking toward that intersection, and of course stopped once I saw the nature of the encounter. I could not see the suspect's hands, and the officer was alone. I crossed the street so I was at an angle to the encounter, and a good 20+ yards away. I knew the suspect was prepping to run (visual cues easy to see if one is used to them), but for some reason, he did not seem to like the idea of running toward us. I considered calling dispatch and requesting another officer, but I was sure they would consider me a crackpot, not someone with a clue. As soon he turned and moved, I called 911 and let them know what I could tell about the direction and that they were in back yards. An officer I know came in to the area, but went too far past the right area, so I moved that direction. It took a moment, but I figured out where they were, and using a phrase I figured the cop would figure out under stress, asked of his well-being. He replied and asked me to stay back, and I did, waving other officers into the right driveway. I later gave a statement, and a couple officers thanked me for paying attention.
I made up my mind that unless I heard a shot, I was not getting closer, as I would probably make it worse. If I could otherwise tell the officer was losing a fight, I would have joined in. (Not as a wrestler - by kicking or shooting the offender in the head. Deadly force either way, yeah, but if the cop is down, easily justified. 11.5EEE boots on a 6'1 235 pound male is darned sure deadly, and I won't care in that situation.) Had the offender come out of that yard alone, I might have deployed the dogs or drawn on him, because that meant the officer was down. This is MY personal decision and comfort level, but I live in the system, I know and teach use of force, and I was willing to set my risk level at a particular point. As I am now retired from LE, the legal standards are looser for me as a private citizen (the 4th amendment does not apply to private citizens, and our statutes track the 4th amendment for cops, but are closer to the old common law rules for civilians). I can articulate my perceptions and reasons for my actions, and I know the local legal climate. One would have to do something completely cuckoo to have a risk of legal problems for helping a cop.