What's the facility's policy? That will direct documentation. Most places require black ink only, however, there are a few old-time places out there that do use the 3 color inks. Black does copy best, but in a pinch, I've used blue. It was blue or NOTHING.
Black or blue but my facility prefers black. I prefer writing my notes on my paper (my brain sheet) in blue but I always sign narcs and any other documentation in black. If no black pen is handy when I need to sign, I'll use blue.
Yeah, back in the "old days" we used black simply because it copied better. Just use whatever color ink your facility wants you to use; mine uses black exclusively. I can write my personal notes with whatever I want to, however.
This day in age it really doesn't matter and many facilities that still use paper have updated their policies to allow black or blue ink. The old thing of "Black copies better" is no longer a modern day concern and is not realistic.