I can't remember the name of a show I saw when I was younger. It was in a library and had some cat and mouse puppets. The mice lived in the wall and there was a train running around the library.

I remember the show also-but not the name.
I believe it was PBS that broadcasted that show...
The closest find is Between the Lions... Sorry.
http://pbskids.org/lions/ OR http://pbskids.org/

Ya, it wasn't Between the Lions, that's what everyone says it is...

Was it Bagpuss? The cat was pink and stripy! If so, this was a British show as far as I remember.

I believe you are looking for a show called Bookmice... You can a little bit of info here Bookmice TV Show (http://www.retrojunk.com/details_tvshows/1965-bookmice/)