Search for a super-mouse

I came home yesterday afternoon to find a mouse peering at me through the glass of the back door. He (or perhaps she) was outside, in our enclosed garden, and I would love to know how he/she got there, although I had no intention of asking. When I walked closer to him, my foot no doubt at his eye level, he ran away; I'm not sure where to. Hopefully from whence he came. He was very fat - perhaps a rat, rather than a mouse? I've gone out into the garden to hang out washing since then and haven't seen him. I have nothing against him as such, but I don't want to see him again. I hope he's gone away.