I think you both have to write one... it says in the booklet that:
"You and your partner must each provide a statement regarding the history of your
relationship, including... The statements written by you and your partner can be on ordinary writing paper..." (booklet 1, page 38, http://www.immi.gov.au/allforms/booklets/1127.pdf
The phrasing does make it sound like you both have to write one. Your fiancee doesn't have to write one as long, or even as detailed--just list the major events and answer the guiding questions provided in the booklet 1. BUT you might want to contact immi directly to see if you could both sign it, along with the cover letter like you said...i would call to make sure because the directions to make it sound like you both have to.
The statements should be certified too.