Do you mean the child has been in the care of another provider and is changing daycares and you want to 'follow up' with the previous provider with a reference on the child?
Yes ~ I have done this. I always ask a client WHY they are changing childcare to get their perspective and than ask for the previous provider contact as a 'follow up' coming at it more so from a perspective of wanting to find out how the child was coping in group care and what strengths and challenges the child might have transitioning to a new program and so forth to help make a more educated choice if my program can meet the child's needs or not.