If there was any doubt that the death was in anyway unnatural it would trigger an inquest to look into the cause of the death. The death certificate would indicate that an inquest had taken place and it would be the Coroner who would register the death and the agreed cause of death from the inquest, which could find the person died from natural causes.
If the Coroner doubted the cause of death he might request a post mortem which if the findings were the person died of natural causes would not then trigger an inquest. Again the Coroner would register the death and the causes as stated in the 'pm'. A sudden unexplained death would be most likely to trigger a pm.
Inquests if they were interesting enough, and there were quite a few of them, would be reported by the local newspaper. Suicides would be more likely to attract such attention. However you don't give any indication from the details of the death certificate that an inquest or even a post mortem took place, or that the local Coroner was in anyway involved.
Though high blood pressure would be one of the main causes of cerebral hemorrhage there are other possible causes such as for instance cirrhosis of the liver or brain tumours, so the family stories that have been passed down may not stem from Charles' final death but events previously when such threats were made. If they were serious enough any such incidences may have attracted the police, who in 1925 were far less interested in domestic violence unless it caused public breaches of the peace, and thus the courts and the newsapapers.
Attempted suicide was illegal so if any previous attempts were made they too would attract the courts' attention. If Charles previously suffered any medical symptoms, depression for instance, it is possible he might have undergone a short stay in an asylum for which the records would hold a detailed case history, so it is worth checking for possible records not just at the time of death but for a few years previously as they may well be a richer source for finding out more about the events that lead up to Charles' death.
Regards
Valda