I had a similar situation - contract to permanent with an agency. However, on contact my agency, they said they would provide everything needed except the job description on the reference letter. Their reasoning for this was simple - they were not present to check if I actually carried out those job duties and will not be able to confirm with CIC if they were contacted. They suggested I contact my now current employer for the job description, which I did, and attached a cover letter explaining this situations. If your agency is willing to give you a letter with all the details you need, go for it, if not, you can contact your supervisor and attach a cover letter explaining why you did so.