I agree with above, I think it's fine to let them sleep on their tummy when they are on your chest because you are there to watch them and you will know if something is wrong...but until you know for sure your baby can control rolling back onto their back consistently it's not a good idea to put them to bed like that because if they have a hard time breathing it will be too late for you to help if you're not awake and watching...You will probably hear a lot of moms tell you that they did it and their babies slept great and they are fine, but my personal opinion is that I would NEVER risk it. My friend's baby died of SIDS at only a week old, so I have seen up close and personal the damage it does and I would never risk it.

Once they are able to flip on the own it's ok but until then put her to sleep on her back