Someone once asked Rumiko Takahashi that, her answer: "I don't think about that, and neither should you"
I don't say you shouldn't ask that, just that the answer is known by no one.
At one point in the manga, Ranma meets the human descendants of animals that were turned into human women via the spring, so the transformation does give you a complete reproductive system. The manga never mentions anyone having their periods, but it's logically something Ranma would have to deal with.