Dr. Matsumoto is a friend of Koudou Yukimura, and a reliable doctor of the Shogunate. He has helped the Shinsengumi on several occasions, giving information or medical help. He's also the one that tells Okita he has tuberculosis. Since he is bald, and so is Dr. Yukimura, it's possible that during that time doctors were required to be bald due to sanitary conditions, or this may be a mere coincidence.