She owns half of the house. You do not own any part of the house. If the house is sold, she would be entitled to a portion of the proceeds. She might be able to force a sale of the house, although this process is complicated. Your legal position is not much different than if you moved into a house that your significant other owned with his mother or brother or anyone else.
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The answer depends partially on how title is held. In CO, ownership is typically either joint tenancy or tenancy in common. In either case, since your significant other is an Owner, he is free to allow anyone he wants to live in his house. I presume that he is making 100% of the house payments. Should the ex-girlfriend insist that the house be sold, then she would be entitled to some portion of the home equity, based on her contribution to the purchase, but that does not preclude your right to live there with your significant other's permission.