I had a 2000 Malibu that had the same problem with the turn signals. It turned out to be the Hazard light switch and something wrong with it. It was covered under a recall but as far as I know the recall only covers the 2000-2001 models. I would give a Chevy dealership a call or call Chevrolet or GM and see if the 2002 year is covered too.
Jimmy 2000 Chevy Malibu 37,000 miles RIP.
August 2005