With the refereeing course fresh in my mind, we were told it's always left backs. Reason being, over time, you get used to the position of your AR and keeping them in your eyeline and where to look for offside calls.
If your question is more related to whether CARs should be with their own defence or attack, unsure whether there is written guidance, but my experience and opinion should always be with their own defence. It's the lesser of two evils if they feel the need to cheat.
I think you have more chance of being credible in over ruling a CAR, especially an excessively flagging one, on their own defence than trying to call an offside that a CAR isn't flagging.
If a CAR misses an offside on their own defence that leads to a goal, the defenders will most likely take it out on the CAR, not you. If the CAR refuses to flag an obvious offside goal for their own team, both you and the CAR are going to get pelters from the opposition.