In this performance the tune is played in the key of G, not D. I've attached a transcription of the bass line, you should be able to figure it out from there. It is mostly roots on the first beat (2nd chord of the head is Gm/F though), and chord types include: Minor, major, half diminished, dominant 7 and the occasional diminished 7 chord. The extensions are not always easy to hear (the piano is very soft) so it's better to stick to the basic triads/7th chords and listen to the melody for extensions and alterations that would sound good.
Attachment 189893 Attachment 189894
