So far I'm mostly seeing these answers by other users: (1) guides to romance and (2) words of advice concerning the ultimate priority of your being a good host. Both are these are extremely relevant. But I'm not sure if any answers touch upon the interplay between host and visitor.
A priori, you don't know anything other than she trusts you with her personal safety and likes you enough as a personal acquaintance. Before assessing your romantic connection, gauge your host-visitor relationship.
Does she want to spend time with you, or time in your region?
That is, are you simply providing a safe stay, or will you two be spending some/the majority/all of the time together? The time spent together will indicate her interest in you as a human, without which there's no reason to think there's an interest in you as a partner.
Let's say she is interested in spending time engaging in activities with you.
Is her focus on the activities, or does it shift to you?
Do you engage in conversation of a personal nature? Essentially, are you bonding? That would be a strong indicator of deeper interest. Do you notice any indicators of interest (as described by Rainbacon)? You can then follow the romantic advice as given in other answers.
How does she carry herself around your house?
This really depends on personality, but is she comfortable dressing down? Does she feel comfortable entering your room and personal spaces? Does she sit beside you on the couch, rug, etc... or away from you? How does she react if you close the space between you? Typically when receiving guest, tacit boundaries are drawn. That is, some might find it odd if you entered "their" room or sat next to "their" pillow if, say, they were sleeping on your couch. So, since you're cohabitating, is she receptive to your sharing personal zones? It'd be a good sign of her physical comfort around you.
In summary, you are a host. Before moving into questions of romance, establish what kind of host she'd like you to be.