Green’s Dictionary of Slang

(US) inquisitive.

1929		M. Levin Reporter 91: What about this pancake story [...] Why, it musta been that snoopy kid that got it.
1953		A.J. Liebling Honest Rainmaker (1991) 71: The greyhounds had faces that reminded her of a snoopy little old schoolteacher.
1980		A. Maupin More Tales of the City (1984) 29: I’ve learned how snoopy you get when you’re loaded.