Gypsy--the wording's not exactly the same, but it sounds like this is the poem you're looking for.

Lin

Why Dogs Leave a Nice Fat Bone
By Anonymous
Source: A Book of Vulgar Verse, copyright 1981 and published by Checkerbooks Inc., Toronto, Canada, ISBN No.: 0-89009-411-X

The dogs once held a meeting
They came from near and far;
Some came in automobiles,
Some came in a car.

But before, inside the hall,
They were allowed to take a look,
They had to take their assholes off,
And hang them on a hook.

They all walked in, one by one,
Mother, son and sire,
But no sooner were they seated
That someone hollered, "Fire!"

Then they all rushed out in a bunch,
They had no time to look;
So each one grabbed an asshole
And ran it off the hook.

They got their assholes all mixed up,
It made them awfully sore.
To think they'd lost the asshole
They'd always worn before.

And that's the reason why
When you go down the street,
A dog will stop and swap a smell
With every dog he meets.

And that's the reason why
A dog will leave a nice fat bone,
To smell another's asshold,
In hopes to find his own.