It doesn't. My brother just passed away about 3-4 months ago. I reported the death to the Police station first, and within the police report yes, it does say lots of thing including the person who report the death, the time of the death and the possible cause of death. This is the procedure in Thailand. Then the body will be transported to the Police Hospital just opposite to the Central world for autopsy. Then within if I remember correctly a few days after the hospital will issue a short report on the cause of death and if the relatives request for a detail report, they will issue it within the next 45 days. If not they will not perform a full examination. (This procedure is of course for a person who does not die by natural causes.) If your father died in the hospital because of sickness, the hospital will then issue
the report on the cause of death itself without having to go through autopsy, if there isn't any dispute.
Then after you receive the hospital report, a relative if possible with the same family name will report to the district office, who will then issue the death certificate (this should be done within a period of time, I think 7 days after the time of death; otherwise it is sort of breaking the law).
I guess you better off seaching for the police report, or the hospital report because these reports will tell you the person who reported death and the cause of death.
The death certificate is only issue to end all the civil rights and obligations; such as duty to pay tax, be drafted into the armed forces, the rights to vote and so on. It is not concerned with the cause and reporter of the death.