Brothers and Sisters!
If you are looking through vital records and cannot find information you thought should be there, do not despair! Not finding the place of birth or parent's names in the records of your direct ancestor, then find those same records for any brothers and sisters. If your great-grandmother's parents are not listed on her death certificate, find the death certificate for her brother or sister and it may be there. Different people know different bits of information at different times! This research method is often called cluster genealogy.
Good luck with your research!