Two suggestions for playing Am & Dm accompaniment...
~     |Am|                        |Dm
strum |^ v   v ^ v | ^ v   v ^ v| |^ v   v ^ v |^ v   v ^ v |
~    3|--0---0-----|------------| |--1---------|------------|
~    3|--1-----1---|------------| |--3---------|--3---------|
~    3|--2-------2-|--2---2-0---| |--2---2-----|--2---------|
~    3|--2---------|--2-------2-| |0-------3-0-|0-0---0-----|
~    3|0-----------|0-----------| |------------|--------3-0-|
~    3|------------|------------| |------------|------------|

the second emphasizes the bass.
~     |Am|                        |Dm
strum |^ v   v ^ v |^ v   v ^ v | |^ v   v ^ v |^ v   v ^ v |
~    3|--0---0-----|------------| |--1---1-----|------------|
~    3|--1---1-----|--1---1-----| |--3---3-----|--3---3-----|
~    3|--2---2-----|--2---2-----| |--2---2-----|--2---2-----|
~    3|--2---2-----|--2---2-----| |0-------3-0-|0-0---0-----|
~    3|0-------3-0-|0-----------| |------------|--------3-0-|
~    3|------------|--------3-0-| |------------|------------|
 

[Am]Muscled, black with steel-green eye
[Dm]Swishing through the rye grass
With [Am]thoughts of mouse-and-apple pie
Tail [Dm]balancing at half mast.
And the [C]Mouse Police [D]Never Sleeps [Dsus4 D Dsus2 D]
[G]lying in the [F]cherry tree. [notes f e f d e f]

[Am]Savage bed foot-warmer
Of purist feline ancestry.
Look out little furry folk!
He's the [Dm]all night working cat
[Am]Eats but one in every ten
[Dm]Leaves the others on the mat.
And the [C]Mouse Police [D]Never Sleeps [Dsus4 D Dsus2 D]
[G]Waiting by the [F]cellar door. [notes f e f d e f]

[Am]Window-box town-crier;
Birth and death registrar.
Instrumental over Am

[Am]With claws that rake a furrow red
[Dm]Licensed to mutilate.
From [Am]warm milk on a lazy day
To [Dm]dawn patrol on hungry hate
No, the [C]Mouse Police [D]Never Sleeps [Dsus4 D Dsus2 D]
[G]Climbing on the [F]ivy. [notes f e f d e f]

[Am]Windy roof-top weathercock
Warm-blooded night on a cold tile.