The most important thing is to listen to your body. Each woman has a different experience with her period, so no blanket rule will make sense to everyone. If doing a vigorous practice with no modifications makes you feel great when you are menstruating, then by all means do that. On the other hand, give yourself permission to take it easy when you have your period if that makes sense to your body.
Many women choose not to during the times of heaviest flow. If you don't want to call attention to yourself by calling out "I have my period!" when the teacher instructs the class to do an inversion, take Goddess Pose - Supta Baddha Konasana in which you lie on your back with the soles of your feet together and your knees falling out to either side. Or if you still want the benefits of the inversion, take Legs up the Wall - Viparita Karani, in which you lie on your back with your butt right at a wall and your legs going up the wall.
Anatomy expert Amy Matthews weighed in with her opinion on this subject when we asked her to tackle the subject of yoga anatomy myths.