An academic, backed by representatives of the Lullaby Trust, has said there is lack of information on the safety of allowing babies to sleep in boxes
Experts have raised doubts around the safety of baby boxes.
In a letter to the British Medical Journal, Prof Peter Blair and colleagues have said the boxes should only be used a temporary bed if nothing else is available.
The boxes contain items including clothing, a play mat, books, a towel and a sling carrier - and the box itself can be used as a sleeping space. The Scottish Government began distributing the boxes to parents 14 months ago.
The Royal College of Midwives wants the scheme rolled out across the UK, saying it offers a "more equal start to life". However the letter, signed by the University of Bristol academic and other representatives of the Lullaby Trust, said there is a lack of evidence into how safe the boxes are for sleeping in.
Compared with cots, bassinets and Moses baskets, it is harder for parents to see their babies easily when they are sleeping in them, they warned.
And some boxes, particularly those that are not laminated, may potentially be flammable or leave babies more vulnerable to pets and young siblings if they are kept on the floor.
Prof Blair said: "One of the things we've been encouraging in the last 25 years is just a bit more closer contact, closer observation. Forget this idea of having infants in a separate room early on.
"Always have the infant in a cot by the parental bed in that room. During day-time sleeps, if the infant wants a nap, try and have the parent in the same room as the infant while that's occurring.
"It's just this idea of observation just in case they get into difficulties. Sometimes you might not be able to do anything about it, sometimes you can, that's what we've encouraged."
Responding to the letter, the Royal College of Midwives pointed out that its position statement on baby boxes had acknowledged that there was limited evidence around them reducing SIDS.
It said that baby boxes needed to be safe, of high quality and the box and mattress should meet at least the minimum UK safety standards.
