This sounds like the Greywalker series by Kat Richardson.
The protagonist of the series, Harper Blaine, is a PI who gained the ability to see ghosts and other supernatural creatures after spending two minutes dead and then being revived.
The supernatural world is referred to as 'The Grey' (hence the title of the series and first book). Near-death (or temporary death) experiences are one of the ways people ever this world.
I couldn't find any references to rich women entering the Grey in any of the story synopses (I have only read the first book), but it could easily be a lesser detail, or from a short story (which would fit with Harper, presumably the 'cop' you remember, being a secondary character), and everything else lines up perfectly.