North Carolina State Laws, Para. 20-124 (f):
"Every semitrailer, or trailer, or separate vehicle, attached by a drawbar or coupling to a towing vehicle, and having a gross weight of two tons, and all house trailers of 1,000 pounds gross weight or more, shall be equipped with brakes controlled or operated by the driver of the towing vehicle, which shall conform to the specifications set forth in subsection (e) of this section and shall be of a type approved by the Commissioner."
I have never found out which (if any) "types" of auxiliary brakes are "Approved by the Commissioner".
North Carolina, AFAIK, is the ONLY state which has such a law. However, as stated elsewhere, many states (and the FMVSS) have "braking performance" laws.
Which, interestingly, brings us to the Section (e) which is referred to above. It states:
"(e) Motor trucks and tractor-trucks with semitrailers attached shall be capable of stopping on a dry, hard, approximately level highway free from loose material at a speed of 20 miles per hour within the following distances: Thirty feet with both hand and service brake applied simultaneously and 50 feet when either is applied separately, except that vehicles maintained and operated permanently for the transportation of property and which were registered in this or any other state or district prior to August, 1929, shall be capable of stopping on a dry, hard, approximately level highway free from loose material at a speed of 20 miles per hour within a distance of 50 feet with both hand and service brake applied simultaneously, and within a distance of 75 feet when either applied separately.
(e1) Every motor truck and truck-tractor with semitrailer attached, shall be equipped with brakes acting on all wheels, except trucks and truck-tractors having three or more axles need not have brakes on the front wheels if manufactured prior to July 25, 1980. However, such trucks and truck-tractors must be capable of complying with the performance requirements of G.S. 20-124(e)."
Of course, that seems to be VERY specific, and it does not appear to relate to RVs towing a vehicle.