Two Dead Boys

Mandi used to tell me the poem of the Two Dead Boys. Unfortunately, she told it differently from the copies they have on the internet. I know the lines but I don't know the lines that fit them together.

Here's the internet version:
"One bright day in the middle of the night
Two dead boys got up to fight
Back to back they faced each other
Drew their swords and shot each other
The deaf policemen heard the noise
They got up and shot the two dead boys
If you don't believe this lie is true
Ask the blind man he saw it too"

But the lines that are missing are these:
"One climbed a tree in the empty lot
The other turned the corner in the middle of the block"

I just can't figure out where they fit and it's critically important!

<3 Sarah