Here's some chord shapes for some of the jazzier chords. 
These are just examples though, so feel free to use other voicings too :)

F13    : 1x123x
A13    : 5x567x
A13sus4: 5x577x
Gm11   : x1x011


[Verse]
Dmaj7
If you're feeling sad and lonely
Dm9                     G7
There's a service I can render
Cmaj7
Tell the one who loves you only
Cm9                  F13
I can be so warm and tender

[Chorus]
Bbmaj7    Gm7
Call me, don't be afraid, you can
Bbmaj7    Gm7
Call me, maybe it's late, but just
Bbmaj7   Gm7          C7      Dmaj7
Call me, tell me, and I'll be around

[Verse]
Dmaj7
When it seems your friends desert you
Dm9               G7
There's somebody thinking of you
Cmaj7
I'm the one who'll never hurt you
Cm9            F13
Maybe that's because I love you

[Chorus]
Bbmaj7    Gm7
Call me, don't be afraid, you can
Bbmaj7    Gm7
Call me, maybe it's late, but just
Bbmaj7   Gm7          C7      Dmaj7
Call me, tell me, and I'll be around

[Bridge]
            Em9  A7
Now don't forget me
             Em9  A7
'Cause if you let me
Dmaj7
I will always stay by you
               Em9  A7
You've got to trust me
              Em9  A7
That's how it must be
Dmaj7                      E7  A13sus  A13
There's so much that I can do

[Verse]
Dmaj7
If you call I'll be right with you
Dm9               G7
You and I should be together
Cmaj7
Take this love I long to give you
Cm9            F13
I'll be at your side forever

[Chorus]
Bbmaj7    Gm7
Call me, don't be afraid, you can
Bbmaj7    Gm7
Call me, maybe it's late, but just
Bbmaj7   Gm7          C7      Dmaj7
Call me, tell me, and I'll be around

[Instrumental]
| Dmaj7      | Dmaj7      | Dm9        | G7         |
| Cmaj7      | Cmaj7      | Cm9        | F13        |
| Gm11 Bbmaj7| Gm11 Bbmaj7| Gm11 Bbmaj7| Gm11 Bbmaj7|
| Gm11 Bbmaj7| Gm11 C7    | Dmaj7      | Dmaj7      |

[Bridge]
            Em9  A7
Now don't forget me
             Em9  A7
'Cause if you let me
Dmaj7
I will always stay by you
               Em9  A7
You've got to trust me
              Em9  A7
That's how it must be
Dmaj7                      E7  A13sus4   A13
There's so much that I can do

[Verse]
Dmaj7
If you call I'll be right with you
Dm9               G7
You and I should be together
Cmaj7
Take this love I long to give you
Cm9            F13
I'll be at your side forever

[Chorus]
Bbmaj7    Gm7
Call me, don't be afraid, you can
Bbmaj7    Gm7
Call me, maybe it's late, but just
Bbmaj7   Gm7          C7      Dmaj7     Dm7
Call me, tell me, and I'll be around