The Bicycle Helmet Safety Institute is reporting of the possible dangers of certain hair syles and wearing a baseball hat under your helmet.

A new hairstyle has appeared in 2001 using hard balls braided into the hair. This style is mostly favored by young afro-american girls and women. It uses balls that are linked with elastic in pairs. Some of the "do's" result in quite a pile of hair and balls.

For helmet fitting, this hair style is about as bad as they get. It has drawbacks:
The thickness of the balls and hair combined under a helmet raises the helmet above the head. The result is that the helmet covers less of the head than it should, leaving the sides unprotected. This is a problem, since studies have shown that a significant number of impacts are occurring below the helmet line anyway, and that the helmets should have more coverage, not less.

Raising the helmet on the head destabilizes it by moving the sides, that normally keep the helmet steady, up and away from the sides of the head. Combined with the loss of coverage from the helmet perched up higher on the head, this is a recipe for disaster in a crash, where the helmet must be stable to remain in position and actually be betweeen the head and the hard place upon impact!

The balls themselves are a potential impact hazard. They may of course shatter in a fall if they are brittle enough and hollow. The shards could cut the scalp. More serious injury might result, however, if the balls did not shatter but instead concentrated the force of the blow on one spot. The helmet is designed to spread out that force to prevent the skull from fracturing. Concentrated impact force from the balls could fracture the skull, and could transmit more g's to the brain whether or not the skull fractures.
In short, we don't think this hair style is suited for helmet use. Unfortunately, braiding hair in this style can take hours, and wearers will be reluctant to take the balls out for a bike ride.

Baseball caps under helmets:
Baseball caps under a helmet pose the same problems as "ball" hairdos. The thickness of the cap and its sweatband, as well as the bill of the cap, interfere with the fit of the helmet. In addition, many baseball caps have a steel ball in the button on the top. That causes all the same problems as the hairdo balls covered above.