The same chord progression all the way through as far as I can tell. 
(G - Bm - Am7 - C) 
The Chorus is the same starting on the C 
(play along with the CD and you'll see what I mean) 
N.B.  You can use Bm7 instead of Bm, it sounds good too. 
 
Intro 
 
(G - Bm - Am7 - C) Twice 
 
Verse 
G                Bm 
how many cabs in new york city, 
Am7           C 
how many angels on a pin 
G                Bm 
how many notes on a saxaphone, 
Am7            C 
how many tears in a bottle of gin 
G                Bm 
how many times did you call my name 
Am7               C 
knock at the door but you couldn't get in 
 
G, Bm, Am7,   C,   G,  Bm,         Am7 
              I know,  I've been,  Careless 
 
I've been wrapped up in a shell 
nothing could get through to me 
Acted like I didn't know, 
I had friends and good family 
I saw worry in your eyes, 
It didn't look like fear to me 
 
I know, I've been, careless 
I lost, my tenderness 
I've been, careless, 
I took, bad care of this 
 
etc. etc.