I would imagine there would be a little delay for the police, then. They might desire the body to remain in the morgue while they investigate. Then you get into procedurals of the time, which I don't really know about. It could be possible that the body might not be released until they felt they had gathered all the information they could from it, but at that time I'm not sure how much they would assume they could get. I really don't know. I would imagine that a week or so might be sufficient. I haven't even read a lot of Agatha Cristie.