Most yoga students are accustomed to hearing their teachers ask whether anyone is menstruating before leading the class into inversions. In many styles of yoga, such as Iyengar, doing inversions during your period is considered strictly verboten. Yet not all teachers consider menstruation an absolute contraindication to going upside down.
From a yogic perspective, the reason for not inverting during menstruation has to do with apana, the hypothesized downward pranic force that is said to help facilitate things such as bowel function, urination, and menstrual flow. The concern is that reversing this normal energetic movement could interfere with the period, leading to a cessation of flow and possibly heavier bleeding later on.
It may be wise to avoid inversions while menstruating. But from a medical standpoint, the belief is based mostly on speculation. Women are often warned that if they invert during their period, "retrograde menstruation" could occur. That is, blood could flow in the opposite direction and lead to endometriosis, a painful condition in which small clusters of uterine cells grow in the abdominal cavity. One study, however, found that retrograde menstruation naturally occurs in 90 percent of women, most of whom never develop endometriosis. So we do not know for sure if inversions increase retrograde flow or whether the backward flow increases the risk of endometriosis.
Here's my take on the situation: During class, if your teacher doesn't think you should be inverting, you ought to comply with her wishes. What you do on your own time during your personal practice, however, is your business.
If you are a seasoned practitioner, I believe you can trust your personal experience. If you choose to invert, notice what happens to your energy level and your menstrual flow. Also, take note of any discomfort you experience. If you don't notice any problems during practice or over the next several hours, I doubt you'll cause any long-term damage. A brief halt in flow followed by normal bleeding isn't much cause for concern. If inverting aggravates your symptoms, though, take it as a sign to back off during future periods.
Adjust your home practice based on your symptoms and experience. As a general rule, you might want to refrain from inverting when your menstrual flow is heavy (when you may not feel that well anyway). With a lighter flow, the risk of going upside down is probably less. Briefly held inversions—say, a minute or less—are also less likely to cause problems than longer-held ones.
Beyond just inversions, don't insist on maintaining a vigorous practice no matter how you feel. If you are tired and achy, your body is telling you to take it easy, in which case my advice is to refrain from all strong asanas—such as Sun Salutations, standing poses, and balances—in favor of a more restorative practice. Sometimes the "real yoga" is knowing when to back off.