I've read on many pest control websites that if you catch a mouse in your home that they must be taken 1+ miles away, otherwise they will easily make their way back to their old home (ie. your house).
I live in a suburban street in an urban part of London. How could a mouse realistically find its way back to my house if I dumped it in the local park, 0.2 miles away?
The unharmed mouse should then be taken 2 miles away from the house and released.
Mind that you should reveal mice at least 1 mile from your house because they can come back to the house easily.
Humane, live-catch traps are something of a pain (mice have a homing instinct, so you have to release them miles away).