crouch around
To move around while squatting. A: "Why are you crouching around your office?" B: "Ugh, I lost an earring."
crouch down
To squat. I crouched down to look for the earring under my desk, but I still couldn't find it.
crouch around
[for people or other creatures] to stoop or squat within an area. Everyone crouched around, hoping the bomb would fall somewhere else. The baboons i crouched around, grooming one another.
crouch down
to stoop or huddle down. Crouch down here, next to me. Suddenly, Tex crouched down and reached for his pistol.