A family in Pennsylvania had their child removed from their care when the mother tested positive for opiates after she had just given birth to her child. The full article can be seen here.
Apparently what had led to the positive drug test was that the mother had eaten poppy seeds on a bagel, poppy being the plant source of opiates. So it is not inconceivable that a woman who gives birth to a child can be drug tested and test positive for the family of drugs that include oxycotin (a potent pain killer which is frequently abused) and heroin, to name just two of the many. Here is a more thorough discussion of how poppy seeds can result in false positive drug tests.
Most hospitals are now required to administer drug tests to mothers of babies in order to protect the children. This is something to consider in terms of what mothers can consume during the course of their pregnancy. It is also something to consider in terms of defending against the removal of a child when the only or primary allegation is that hte mother tested positive for opiates at the time she gave birth.