Generally speaking, MOST states allow private citizens to make arrests. If a citizen KNOWS that a felony has, indeed, taken place, they would most likely be covered. If it is only a "perceived" felony, then it might be some rough going.
Violent misdemeanor crimes are an "iffy" topic, especially if something such as "mutual combat" is involved (two people fighting, with one of them obviously beating the snot out of the other. Of course, that might lead to a FELONY, if "great bodily injury" has been inflicted).
By identifying yourself as a police officer when you are NOT one might cause you much grief. However, if you're LEGALLY armed and come upon an ARMED robbery in progress, I don't see anything wrong with DEFENDING yourself or any other citizen! Heck, in that situation, a commanding "Drop your gun or you're DEAD!" might be totally permissable.
You don't have to dance around the "political correctness" usage of words in a life-or-death situation.
Lastly, most citizen-involved shootings depend upon "articulation" of the facts. Let's say that you are a "concerned" citizen that has chosen to be armed, even though illegally, due to the high crime rate in your neighborhood. Well, that would make you sound like a "vigilante". On the other hand, if you were carrying illegally, but could give a "reasonable" story as to why you were armed, it might be "reasonable" enough for the court!
I spent 31 years in law enforcement, and KNOW how effective "command presence" is. I've had bad guys drop guns just by using "command presence"! It's a matter of using a serious-toned, authoritative-sounding command that makes the bad guys into "believers". I never resorted to using foul language (i.e., "Drop the gun, *******!"), for I always chose to sound "professional" and "confident". Besides, why stoop to the same level as a bad guy?
I'm sort of on a "fenceline", for I am now a RETIRED police officer, but still legally carry. If I happen upon an armed robbery in-progress, I could care less about "political correctness". I'm not going to waste my breath by using the word "retired"....it will be "Police officer, drop the gun!" I will ARTICULATE my word usage LATER, after I have successfully (hopefully) defended MY life and the intended robbery victim. "NO, I didn't tell the bad guy that I was a retired police officer! My training and 31 years of experience just kicked into high gear when I yelled 'Police officer'!"
Lastly, having been VERY pro-active for gun rights and CCW "priveleges" for citizens, I sure hope that you who have carry permits aren't merely concerned about your OWN rear-sides! It would devastate you if were able to do "something" to save someone else, but did nothing! Hey, I was PAID to "protect and serve", but I'll STILL come to your aid if I am able to do so....free gratis!
I almost forgot about one particular "police impersonator" that I had the PLEASURE of meeting as a LEO. He identified himself as an "FBI agent" to me, and he LOOKED it....but he didn't have any ID at the time (he was a beach-goer, clad in swim trunks). He explained that he had just observed a child molestation on the beach, and took us to where the suspect and victim were. The victim (a 12-year old boy) was too scare to run away from the suspect, who had reached inside of the boys swim trunks to fondle him. The statements that the victim and the "FBI agent" gave us corroborated the incident, and the suspect was taken into custody. He had a LONG arrest record for child molestation. He should have been locked up FOREVER!
When the trial came up, the "FBI agent" took the stand and testified VERY professionally! When asked about his "FBI" status, he stated that he was on a "sabbatical leave" from the agency. VERY convincing, and the child molester was convicted.
When I stepped out of the court room, a REAL FBI agent approached me, and filled me in. The "witness" was NOT an FBI agent, but had applied for employment with the FBI at one time. He was actually an insurance salesman! When the impersonator came out of court, the REAL FBI agent and myself confronted him. His claim was that he thought that an "FBI agent" status would be more credible than that of an insurance salesman. We walked the impersonator back inside the court, requested to meet with the Judge, and were escorted into the Judge's chamber. The Judge was VERY understanding, and said that the FACTS of the case had justifed the actions of ANY citizen. The Judge also left it to the REAL FBI agent, whether any charges of "impersonating" would be filed. In essence, the child molestor was STILL "guilty", no matter what!
The REAL FBI agent had a LONG talk with the insurance salesman. Fortunately, the impersonator hadn't "detained" the child molestor in any way, and hadn't received any "gratuities" for having impersonated a LEO, so his impersonation could be "overlooked". Fortunately, the defense attorney for the child molestor NEVER caught wind of the situation, or it might have been tossed out of court!
Score? One child molester convicted and sent to prison, one "FBI agent" impersonator being caught and released....patted on the back, but chastised at the same time, and ME, pleased that the outcome of the trial had been positive!