No reference, just like there is no reference regarding a requirement to take it with the feds. Each FSDO has the authorization to make rules regarding practical exams (ex: Ours doesn't allow self-examining authority for 141 schools). Ours is usually too short-staffed to administer them. In fact, it probably would have been cheaper for me to take it with a DPE versus waiting over a month for an inspector.

When taking any practical exam ANY material required for a rating you currently hold is fair game. Based on the requirements for a CFII (or CFI for that matter) they could ask you private questions as well. I did an ILS on my CFI initial based on the examiner's rationale of "what if you inadvertantly wandered into IMC?"