CRS statement is in small print form on all paperwork relating to aircraft maintenance that will form part of the maintenance task, schedualed or unschedualed. This statement is stamped by an approval holder. (The equivalent of oversignatures in RAF speak, except that the approval holder is legally responsible for work carryed out). Approval holders are licensed in the relavent category, and approved by the company they work for. To hold an approval you need to pass an oral exam, usually of company procedures, and a few 'You find your self in deep doggy doo doos. How can you leagally dig your self out?' type questions. And it can be a total mine field.
CMR is usually signed by a dual licensed engineer with 8 years experience in a supervisory role, working in the Airworthiness department. This is carried out every 3 months or sooner if the CAA deem it to be necessary, and is a paperwork exercise to prove that all maintenance has been carried out, and that all tasks have been recorded correctly. I remember once that a Dupilcate Inspection (Independent in RAF speak) was missed on a thrust reverser and all Hell broke loose. But it was soon rectified.
I Hope that this has been of some benifit to you. Good luck with your civilian career, but remember above all else, when you go into Civvie Street you are Mr. Forget about the RAF as you will be starting afresh, and although you may have been an NCO when you were in, you are not one when you leave. Be perpared to be 'One of the Lads' for at least 6 months before you go for your approval as it may take you that long to get your head round the civilian system.