Umi no Yami, Tsuki no Kage (1989)

Darkness of the Sea, Shadow of the Moon

Ruka and Rumi Kobayakawa are twin sisters in love with the same man, athletic upperclassman Katsuyuki Touma. Rumi seems supportive of Ruka's fledgling romance with Katsuyuki, until the twins are infected with a strange bacterium that transforms Rumi's personality and gifts the twins with terrifying psychic powers. Now Rumi will stop at nothing - or no one, that gets between her and Katsuyuki, including her own twin sister... (Source: ANN)