A drawstring should not be used in the neck of a baby's garment. Such a string is dangerous, for it may get pulled too tight about the baby's neck and strangle him. Long ribbons, sometimes used as trimming on babies' clothing, are undesirable for the same reason.
This statement came from a government publication published about 1949. The only difference between then and now is that the Consumer Product Safety Commission has issued guidelines (links to a PDF) for children's outerwear (2T-16). Drawstrings are not permitted in clothing for this age group. While the agency does not include infants, it is almost a given that the same guidelines would apply. The drawstring issue is a continual battle. The CPSC issued a recall notice as recently as April 2007. So please be careful.
The chapter also mentions oft over-looked safety issues such as snaps and buttons. Snaps or buttons which easily pull off are considered choking hazards and the CPSC will issue recalls for items that fail. Buttons can break during laundering. If the wrong type of snap is used or the snaps are improperly applied, they can fall apart or pull out of the fabric. So test, test, test.
Finally, the chapter mentions the use of safety pins. In the past, safety pins have been used with cloth diapers. But any trimming attached with a safety pin is a big no-no. They are not only a potential choking hazard, but also a poking hazard. And yes, I have seen manufacturers try to use regular safety pins to attach trims. This is a picture of an acceptable pinback which may be used to attach removable trims such as silk flowers:
This pinback is nickel and has a safety latch. The sharp point is covered. It can either be hot-glued or stitched securely to an item.