sleeping positions

Sarah
Does anyone's baby sleep on their side ? I have been wanting to transition my three month old to the crib and she hates being on her back (reflux) and today I tried her on her belly she liked it for maybe five minutes I put her on her side and she instantly fell asleep.
Her one arm is positioned so she can't roll on her belly .. and I have towels rolls on either side of her underneath the crib sheet  to limit rolling .