Well, no one can disparage your
courtesy (I'm sure that your Mom is proud, and I'm not making a joke), but I really have to question your thought process regarding this issue. If you saw a mugging or a purse snatching, which of the following ways would be more effective in obtaining law enforcement response:
1. Excuse me, Officer. I just witnessed a purse snatching. The victim doesn't appear injured. The assailant was a (fit favorite description here) and he took off in an easterly direction on Main Street. It happened about thirty seconds ago.
2. Excuse me, Officer. Before I say anything, please allow me to inform you that I have a concealed carry permit, and I am currently armed. Pardon? Yes, I currently have a pistol on my person. What's that? Oh, yes, it is in an in-waistband holster at four o'clock on my right hand side. Pardon? You want to disarm me before we speak? Sure, but I should tell you..... Oh, okay, against that wall? Okay. (officer pats you down, and disarms you) Just curious, but why do you need to disarm me? For my safety and for yours? Well.... okay. Anyway, I just..... ummm, yes, I do have some identification. Yeah, my license and permit are here in my wallet, but..... Okay, here you go. (officer calls in your information) What was my question? Oh, yeah! I just witnessed a purse snatching. The victim doesn't appear injured. The assailant was a (fit favorite description here) and he took off in an easterly direction on Main Street. It happened about, well, I guess about seven or eight minutes ago.
Neither one of the above situations involve any wrongdoing by you or the officer involved, but the second option was considerably less efficient.
As for a knock on your door, that is your private property. I am not sure about your state, but here in Connecticut if the police knock on my door without me calling and requesting their response, they will be met with me and Mr. Steyr on my hip. In fact, without a warrant, they won't even get to come inside. All the while being respectful, of course. Imagine this clip, plus Mr. Steyr on the Hip (only IF it is legal in your location):
YouTube - How do I keep police from entering my home?