I'm going to give a warning here of unpleasant subject matter concerning death and circumstances around deaths.
I used to volunteer in the Coroner's Officer's Office. Most COs are police or medical background. The ones I worked with were police staff, having retired from the force as inspector rank. They were the ones who took 'possession' of a dead body on behalf of the crown (the Coroner themselves are the Crown's representative). This meant literally they would be on the scene of unexpected death recovering the body usually with help of an undertaker. This would include RTAs, suicides, victims of suspicious circumstances, and of course many natural but unexpected deaths, including repatriation of those who have died overseas. I would not like to do it. In one weekend one of them attended a suicide, an RTA and suspected murder case.
They then arrange post-mortem if necessary, follow the paperwork through and liaise with the families and undertakers for release of body and often doctors and other medical staff. They provide evidence to inquests. The coroner has his own clerical staff (ours was a solicitor, but again they could have a medical background) who run the inquests, so there is liaison with them too. There is a lot of distressing material. But someone has to do it, and they were very respectful throughout.
I've probably missed loads of what they do, but if you don't have experience (and resilience) of attending traumatic scenes, I think it would be unlikely you'd succeed in getting the job. Unless it's organised very differently in your locality and the role covers a different range of work.