Asian Movie involving a scene with a murderer and a child coming face to face on the side of a road

I found it. The movie is Memories of Murder (2003). Its a South Korean film.

I got the scene I described in the Question a bit muddled up. I found the description of the scene on wikipedia. The description below is a major spoiler so beware.

Visiting the crime scene years later in 2003, Park Doo-man, now a businessman, learns from a little girl that the scene had recently been visited by another, unknown man with a 'plain' face. The little girl had asked him why that man was looking at a drain (from the scene of the second murder, which is shown at the start of the film), and he told her that he was reminiscing about something he did there a long time ago.

The film looks very interesting so should be well worth a watch.