Since it’s over 75 years you can contact Lothian Health Services Archives and ask to see the records.
I did this for an ancestor who had died in The Royal Edinburgh Hospital (psychiatric) in the 1930s aged 20 years.
I had to go to the University Library to read them, this was about 10 years ago. They were very detailed including the PM.
I’d say now with todays knowledge it was glaringly obvious he died of sepsis but this was not so understood then hence due to the infection and his ‘ravings’ he ended his short days in the psychiatric hospital.
If you contact them and find there are records and if you are not able to get a copy of them I am happy to go to the designated place to make a copy as I’m in Edinburgh.
Newspaper intimations as suggested by GR2 would be a good way to go, both in Edinburgh and her home town
Good luck