I consulted Definition 1, in which the definition and examples are ambiguous about the connotation. Yet Definition 1.2 is surely negative: '...to be rid ....'
So what's the connotation? I thought to include another example from p 63, Ward Farnsworth:
Your defense comes from federal law, but my initial claim against you doesn’t. So the case is consigned to the state courts.
I also consulted http://www.etymonline.com/index.php?allowed_in_frame=0&search=consign&searchmode=none; the etymology for 'consign' is partially:
from com- "together" (see com-) + signare "to sign, mark," from signum "sign"
This suggests an air of officialdom and austerity, but is this true presently?