No, cats are not baby killers. They dont steal anyones breath and theyree not plotting to injure your sleeping infant. This ridiculous myth probably started because some cats enjoyed curling up next to the warmth of babies. A cat may even have sniffed the babys mouth due to the scent of milk on the breath and that act probably set off alarm bells in the minds of panicked parents.
What we now know of as SIDS (sudden infant death syndrome) may have been blamed on cats who enjoyed sharing a nap with an infant.
Because infants cant turn to get away from objects, its not safe to have ANYTHING in the crib or bassinet with the baby and that includes a blanket, toy or stuffed animal. So for safety, keep your cat out of the crib but certainly allow your cat to enjoy being close to your baby at other times.
There are crib tents available that make it easy to keep the cat out of the crib.