That's what I thought at first but after seeing the car scene just like what the comment above said, it looks the girl was just crazy and obsessive and probably wanted to end both of their lives so they can be together forever but Taemin survived and the ghost girl probably still can't remember what happened. And the fact that Taemin never introduced her to anyone before maybe one of the reasons is that.
But still... the author might pull something clever like it was the other way round. And making us all think that Taemin is a good guy.

this is the first time he’s ever made that face. I’m 10000% sure he killed the ex and wants her gone(“in life and death”).