probably should not. if there is no need to, then avoid it at all costs. it'll make things awkward if you just say it randomly. even if you're talking about periods already, it'll still be awkward if you say "hey I'm on my period!"... "uhhhhh...."
From the little that I understood of that questions is that you're seeing if you should tell somebody that you're on your period. Answer is, no you probably shouldn't it's a private girls thing that few people should know about.
Trust me. Guys REALLY don't want to know that. The only time you should tell a guy that you were on your period is if he is a judge and he asks you why you stabbed your friend 37 in the eye with an ice pick, then ran over him with a large construction vehicle. Other than that, just keep the whole period on the down-low, OK?