You need bowhunter ed to apply for or hunt the archery-only tags.
If it's a general any-weapon tag, you don't unless you're younger than a certain age that I can't remember off of the top of my head. I'm 38 and the age was significantly younger than I am. There was a change about a year ago to make it mandatory to have bowhunter ed for every bowhunter, but then they changed it to everyone born after a certain date. Sorry, I don't have the date. It was in the late 80s or early 90s... I can't remember.