Is it more likely that the cat brings in mice which is why they are occasionally found in the house (live), or do they find their own way in for warmth? It is only the odd mouse, and no evidence of occupation (droppings, nests, nibbled things etc!) has been found. The cat seems to be quite a good mouser so I know she does bring them in - dead or mangled.
I found one living quite happily behind the bath panel.I didn`t know it was there till I went for a new bar of soap and thats what it had been living on. The last place I would have thought to look.
As a Pest Controller I would say that cats are more likely to bring mice in than they are to catch them once they get in.
70% of people I go to with mouse problems have got cats, cats like to catch them and bring them indoors to play with, they then drop them and the mouse runs under a fridge or something and the cat can no longer find it.
They will also find there own way in, one way or another.