The rule is that any bar used (flat, flared, drop etc) be no wider than 50cm.
As to how strict they are it's virtually impossible to police. There's not much in the way of formal bike checks (plenty of people wandering round with tape measures and a tyre width checker) but so many people swap bikes on various parts of the course (another thing I think should be banned) that some of the front runners are using almost road bikes on the road sections and swapping to bikes of dubious legality for the off-road bits. I've seen people on bikes with tyres that are obviously >35mm yet by the time they come back into the finish they're on a regular CX again having swapped it back again. I think it should eb like a mountain bike race in that respect - no bike swaps, no wheel changes, you should be self-sufficient while on course. It would cut down the amount of traffic as well, cars hurtling past with bikes on board, desperate to catch up to their rider so they can swap the bike back again.