MadMarchHare,
Scotland does not have coroner's inquests.
However, cases of sudden, unexplained or suspicious death are investigated by the Procurator Fiscal. The PF carries out what is referred to in Scotland as a Precognition - which is (in this particular sense of the word), as SandraC said, a preliminary examination of witnesses and relevant people - in order to determine whether the matter should go to trial.
Precognitions are, of course, not limited to deaths but apply to any matter where there is a need to determine whether there should be a criminal prosecution. I have pages and pages of the records of a precognition in the case of a person who ended up being prosecuted for (and, in 1848, convicted of) the crime of forgery and uttering.
You can read more about the Office of the Procurator Fiscal at:
http://www.procuratorfiscal.gov.uk/AboutRegards,
JAP
PS: The above site has a search facility. If you search for 'precognition' it leads you to a PDF document which explains modern day precognitions.