Cats and newborns

Hi ladies, I have a newborn and my SO has a cat. Im not a cat person whatsoever so I have no experience with them. I've heard scary things regarding cats and babies and today I saw the cat looking as if he was going to jump in my baby's bassinet, twice. I'm not sure if this is because he was never introduced to baby or if there is more meaning behind this. If you have cats and children, please let me know how your experience was and what I can do to always assure my baby is safe.

p.s I never leave my child unattended.