This is covered under Administrative Code Sec. 203.2, which states the victim's family isn't responsible for the cost of transportation of the body TO an autopsy, storage, etc. (i.e. the county picks up the tab).

We've got a local funeral director who interprets this as the county being liable for transportation costs to AND FROM the autopsy (i.e. he knows the county will pay him, but has doubts about his customers).