Well, I don't know how long she's been in your house. I'm assuming a short period, so this is based on that.
I would suggest love and patience, above all else. We were screwed up before we came to Christ; coming to Christ doesn't mean we're no longer screwed up, but we are on the road to recovery. Sanctification is a process. Show this girl some trust and soon she will trust you as well.
If she is without a job and without money then the time will come soon that she will have to talk to you about this. Give her the opportunity to approach you'all first. If you confront her with knowledge she didn't provide she will think you are spying on her and then she will never trust you.
Obviously there is a time limit on this approach, but in love and patience let Him (the Lord) show you when that is... and even then, approaching her in love is the key, lest you turn her from the Lord.