It seems this rhyme is an adaptation of a Jane Taylor poem. (That's what you can hear sung in the mp3.) Here's the poem:

I LIKE LITTLE PUSSY
By Jane Taylor

I like little Pussy,
Her coat is so warm;
And if I don't hurt her
She'll do me no harm.
So I'll not pull her tail,
Nor drive her away,
But Pussy and I
Very gently will play;
She shall sit by my side,
And I'll give her some food;
And she'll love me because
I am gentle and good.
I'll pat little Pussy,
And then she will purr,
And thus show her thanks
For my kindness to her;
I'll not pinch her ears,
Nor tread on her paw,
Lest I should provoke her
To use her sharp claw;
I never will vex her,
Nor make her displeased,
For Pussy can't bear
To be worried or teased.

Here's a slight variation of the rhyme from The Nursery Rhyme Book, edited by Andrew Lang and illustrated by L. Leslie Brooke (1897):

I love little pussy, her coat is so warm;
And if I don't hurt her she'll do me no harm.
So I'll not pull her tail nor drive her away,
But pussy and I very gently will play.

Here's a slightly different version from The Little Mother Goose (1912), illustrated by Jessie Willcox Smith:

I like little pussy,
Her coat is so warm,
And if I don't hurt her,
She'll do me no harm;
So I'll not pull her tail,
Nor drive her away,
But pussy and I
Very gently will play.

This version of the rhyme is found in A History of Nursery Rhymes (1899) by Percy B. Green. The 1st illustration is from The Real Mother Goose (1916), illustrated by Blanche Fisher Wright, and the 2nd illustration is from The Nursery Rhyme Book, edited by Andrew Lang and illustrated by L. Leslie Brooke (1897). The 3rd illustration is from The Little Mother Goose (1912), illustrated by Jessie Willcox Smith. 4th illustration is by H. Willebeck Le Mair from Our Old Nursery Rhymes (1911), arranged by Alfred Moffat.

Sung by Ruth Golding for Librivox.

2nd mp3 recording performed by 17 talented university student musicians who were sisters in the Sigma Alpha Iota International Music Fraternity for Women at California State University-Stanislaus in 2007. The musical score the recording is based on comes from Our Old Nursery Rhymes (1911) arranged by Alfred Moffat.