Some religions take their beliefs about autopsies very seriously. It's also possible that they know why she died. For example, if she had undergone a liver transplant and was in poor health as a result, it would be pretty obvious to them what the cause of death was.I know but it seemed suspicious that after she died her family didn't want to find out why she died after they found her. But if you look at her body from a distance and it's more or less obvious why she died, and if they know the girls are sick, they can more or less guess why she died. I guess I watch too many detective and American murder mystery movies.
To answer your earlier question, yes, families can refuse an autopsy unless the police have some evidence of foul play. As long as the police are satisfied that their death wasn't the result of a malicious act, the family can choose what to do or not do.