Here's a dilemna for those two girls: they got only one body to share... I do wonder who controls the body though, hehehe
In my opnion, they both have control over the body. They're not sisters, and not even friends to begin with... but considering their condition, they had to form bonds of friendship. Also, they can't connect any head with the body, though they made some collars that reunite the head and neck, so they have to bring their heads with them everywhere. That's why they often bring a bag.
For sure it can leads to awkward situations, especially when they get angry at each other, but heh, that's life. At the end they're friends and they deal with their strange life, no matter what.