Transcript:
Charlie Brown is walking next to Snoopy and says "Go home, Snoopy! Go home!!"
He turns to Snoopy and continues, "Go home, I saw! Stop following me!!" as Patty looks on questioningly
Patty comes over and says "He's not following you... he lives in that direction!"
Charlie Brown continues on upset next to a smiling Snoopy
It's pretty unclear, Snoopy seems to live with whoever's convenient for the joke setup to work. Here's a smattering of early strips that imply various owners/houses: