Having a mouse is a stressful situation, even if it is an endangered species.
To catch the mouse, I would try raisins and/or chocolate and use a trap that will allow you to release the mouse, instead of the traditional kind of mouse trap. Try experimenting with different foods such as a vegetable.
You might take a close look at the mouse to rule out whether it is a more common field mouse, too. Then you would not have to worry about destroying the mouse if that were to happen. Good luck!
There are safe Humane traps as seen in this link: http://www.themousedepot.com/ It can be baited with cheerios, a little bread and butter, a banana chip, a rodent safe treat that can be purchased at the Pet supply or a small piece of hard boiled egg. Please do not use Chocolcate to bait the trap, since that is toxic to all animals and would be defeating the purpose of trying to safely catch the mouse. Patience and the right treat should lure the little mouse into the safe trap.
Once you cath the mouse you can take it to any humane society or the Department of Natural Resources and they can identify the species and make sure that it is a rare species, or dispose of it humanely. Harvest Mice are generally found in the UK, but it is possible that you may have found one that had been brought in.
Thank you Joan, that's just what I was looking for; I appreciate the link to the mouse depot, that's helpful. I didn't know chocolate is poisonous except to dogs, that's also good to know!