Not all women feel the same during menstruation. Some feel like sitting on the couch cuddled up with a heating pad and a pint of Ben & Jerry's, and others have tons of energy to go for a run. I'm a firm believer in listening to your body, but I also know that a little exercise can help alleviate cramps (and your rotten mood).
Doing yoga is great when you have your period because the movements are slow and gentle, and leave you feeling completely relaxed. The ongoing debate though is whether or not a menstruating woman should do inversions such as shoulderstand, headstand, forearm stand or handstand.
Some instructors think inversions disrupt the natural flow of your period, that it can cause retrograde menstruation, where blood flows in the opposite direction and can cause endometriosis. However, there is no scientific evidence that inversions can cause this.
Also, you're only upside down for a couple of minutes, so can that short amount of time really affect your flow that dramatically? Only you can answer that question. It all goes back to doing what is right for your body. If inversions give you energy and make your period symptoms more bearable, then I say go for it. On the other hand, if inversions put pressure on your uterus or make you feel dizzy or lightheaded, skip them. This applies whether you have your period or not. Yoga is all about feeling good, so do what feels right to you at that moment, and don't let anyone make those decisions for you.