Locked. You'll have to pick or bash the door to get in to get the quest, but oddly the woman isn't upset that you broke her door down.
It's been a while for me, but I'm nearly certain I've completed that quest (a number of times, even!) and I don't remember having to pick or bash a door to do so.
_______________________________________________ "When Boba Fett told Darth Vader, "As you wish," what he meant was, "I love you.""