Whatever you do, DO NOT do what my (thankfully former) apartment manager did, and just toss rat poison up there and ignore it from then on out. The mice died up there and it was HORRIBLE. We literally had maggots falling through our lights after they were feeding on the dead mice, and the apartment manager didn't do anything about it. It was a horrible experience that I still have nightmares about. Luckily, our current apartment manager seems to be okay.
Now I am going to have nightmares about this!