If it has overdrive it is most likely a 700R4 transmission, if it doesn't,it is most likely a 350 turbo.
Assuming it is automatic, read the dipstick, probably Dextron III.
The 2001 Chevrolet Impala has a 4-speed automatic.
The 2002 Chevrolet Impala has a 4-speed automatic.
The 2004 Chevrolet Impala has a 4-speed automatic.
The 2006 Chevrolet Impala has a 4-speed automatic.
The 2009 Chevrolet Impala has a 4-speed automatic.
The 2012 Chevrolet Impala has a 6-speed automatic.
The 2005 Chevrolet Impala has a 4-speed automatic.
The 2003 Chevrolet Impala has a 4-speed automatic.
The 2007 Chevrolet Impala has a 4-speed automatic.
The 2013 Chevrolet Impala has a 6-speed automatic.
The 2008 Chevrolet Impala has a 4-speed automatic.