A Death Certificate has been issued. Law Enforcement wouldn't release the body without a death certificate. A Death Certificate is a pretty important legal document. A Funeral Home can't have a funeral service, cremate a body in their possession without a death certificate. I doubt law enforcement will release a death certificate to the public, at this moment, it may be under seal as well.
The key report to find what happened to Heidi Broussard is the autopsy report. The prosecution's case against Heidi Broussard will have the autopsy report as the foundation for their case. The toxicology report will also be crucial. Heidi's family and Shane Carey will need a death certificate or many official copies, to close Heidi's bank account, transfer car titles, close credit cards, validate custody forms for Heidi's two surviving children, but I doubt the death certificate will be release publicly right now.