Like said above, check the owners manual. However...with one or two Chevy models, even that might not be enough.
I remember here on the Forum, something about a mid-year change of transmissions...the car went from towable to not towable (4-down) and several trannys "blew up"...however, GM supposily made good on this.
Research that here on the Forum.
I personally tow a 2007 Chevy HHR auto, and a 2011 Ford Ranger 4WD auto with no problems. The HHR, pull a fuse. The Ranger needed a "transfer case disconnect kit". (Strange,how Ford 2WD automatics are NOT towable 4 down at all.)