There is some limited evidence that intranasal oxytocin ameliorates postpartum depression. I am interested in publications, clinical anecdotes, personal reflections, etc.
I would think it would not depend on why the woman is depressed. It is means of no sense that Oxytocin receptors are not affecting to the body of postmartem then it may not work, even if it is tried.
In Sweden they give oxytocin spray to the mother of the new born to improve the breastfeeding process. For some women non-functioning breastfeeding is a stress factor. For some women low oxytocin level is a risk factor for post-partum blues. All the possible benefits of the hormon is worth finding out. The “cuddle hormone” or the “hormone of love,” oxytocin is known for its ability to foster feelings of bonding and attachment.
See: Mah, B. L., Van IJzendoorn, M. H., Smith, R., & Bakermans-Kranenburg, M. J. (2013). Oxytocin in postnatally depressed mothers: its influence on mood and expressed emotion. Progress in Neuro-Psychopharmacology and Biological Psychiatry, 40, 267-272.
Make sure that no matter what, the mother and baby spend time together each and every day in the postpartum period. Otherwise, the mother starts to grieve that she "lost" her baby.