There's an old wive's tale that one should not let a cat in a room with a sleeping baby.
Apparently over decades / centuries / millennia enough babies have suffocated when a cat tried to sleep on this nice warm object, to generate this old wive's tale.
But since it's just an old wive's tale it cannot be counted as any kind of rational scientific evidence.
After all, anecdotes are not evidence.
I do know my cats used to get in bed with me, which was OK, but then their purring while they settled in for comfort and their "kneading" me kept me awake for a while.
"Soft kitty, warm kitty,
Little ball of fur,
Happy kitty, sleepy kitty,
Purr, purr, purr."
Terry, 230RN
REF (SIDS. This Mayo Clinic article on
Sudden
Infant
Death
Syndrome emphasizes that it's still a bit of mystery (or has multiple possible causes), but does mention sleeping with pets as a risk factor):
https://www.mayoclinic.org/diseases-conditions/sudden-infant-death-syndrome/symptoms-causes/syc-20352800