Words and music Bob Dylan.
Released on Oh Mercy (1989) and in a live version on Unplugged (1995).
Tabbed by Eyolf Østrem

B” (in the bridge) is a chord with a whole lot of tones in it, on several guitars, playing quite different chords. A good approximation is x22324.

In the outtake version the song is clearly played in C, with a capo on the 4th fret (see below). On Unplugged Dylan plays his licks without a capo, while Jackson uses the capo on the 4th fret.

E   E/g#  A    E
E   E/g#  A
A   B     E    A
E   E/g#  A    E

       E               E/g#
Seen a shooting star tonight
      A              E
And I thought of you
E                               E/g#
You were trying to break into another world
  A
A world I never knew
A                B
I always kind of wondered
       E            A
if you ever made it through
       E               E/g#
Seen a shooting star tonight
      A             E
And I thought of you.

Seen a shooting star tonight
And I thought of me
If I was still the same If I ever became
what you wanted me to be
Did I miss the mark or overstep the line
that only you could see
Seen a shooting star tonight
And I thought of me.

C#m                  /c
Listen to the engine listen to the bell
/b                    /a#
As the last firetruck from hell
A                B                   E
goes rolling by, all good people are praying
         C#m                 /c
It's the last temptation the last account
         /b                      /a#
The last time you might hear the sermon on the mount
A                 B”
The last radio is playing.

Seen a shooting star tonight slip away
Tomorrow will be another day
Guess it's too late to say the things to you
that you needed to hear me say
Seen a shooting star tonight slip away.

Capoed version (capo 4th fret) 

       C               C/e
Seen a shooting star tonight
      F              C
And I thought of you
C                               C/e
You were trying to break into another world
  F
A world I never knew
F                G
I always kind of wondered
       C            F
if you ever made it through
       C               C/e
Seen a shooting star tonight
      F             C
And I thought of you.

...

Am                   /g#
Listen to the engine listen to the bell
/g                    /f#
As the last firetruck from hell
F                G                         C
goes rolling by, all good people are praying
         Am                  /g#
It's the last temptation the last account
         /g                      /f#
The last time you might hear the sermon on the mount
F                 F/g
The last radio is playing.

(The Unplugged version has

F                 D9
The last radio is playing.

with D9 = x57555 or something like that.

Also the Fs are occasionally played Fmaj7 (133210)