I'm surprised that (unless I missed it) nobody has advised this tenant to call the Board of Health -- or whoever it is who responds to rodent complaints. This is a serious issue. It is the LL's duty to do what is necessary to ensure that the tenant has no mice--plugging with steel wool every crevice big enough to accomodate a pencil, putting guards over the doors, etc. etc.
Also, since this is a stabilized apt., this really belongs in the rent stabilized apt. board.