There's a fucking mouse in my house.

Ok I know I have an apartment, and I've been trying for almost a week to pretend that it wasn't there. I know you wondering how one can pretend something is not there, but before last night I hadn't actually seen the stupid thing. See I guess its NOT actually in my house per say, however its seems to live in the entry way to my front door. I noticed the other day there were paper towels and a rock outside my front door that appear to have come out of the hole in the frame. Now I was pretending because I didn't stuff paper towels in there. I was trying to assume that whoever live here before me would not actually think that a viable option to fill the whole, but apparently I give them too much credit. Anyways, like I said I was pretending that it wasn't there, being that I hadn't actually seen it.
Well last night I opened up the door and turned on the light, and this little thing crawled out of the air conditioning. Then it proceeded to crawl up into a whole that I would guess goes under the stairs to the apartment above mine. Ish. I do actually have all my christmas stuff out there and now I'm not sure I will be touching any of that anytime soon. Hope it doesn't get really hot because I'm sooooo not touching the Air conditioner, which I think I might now actually be afraid of.
I really don't know what to do about the mouse becuase I don't think I can do the whole trap thing, and I'll be real honest and say that Idon't know how else to get rid of it. I mean seriously if filling the whole with paper towels didn't work I really don't know what will. On the plus side I'm happy that it was not a rat. As I was kind of freaked out at the idea of a rat being in my house. Ever since I saw this HUGE ASS rat run across the street and down the alleyway between my building and the building next to mine.
Seriously I just want a normal apartment where the only living things are people. Is that really too much to ask. You would think not but apparently it is.