Do I need to file an amended return?

My employer sent me a corrected W2 because they made an error in Box 16 as described in this discussion. Essentially, some income that should have been reported as earnings in both Minnesota and Wisconsin was only reported as Minnesota earnings.

 

The correction does not change anything in terms of what I owe or will be refunded. Do I still need to file an amended return? If so, do I need to amend all three returns (Federal, Minnesota, and Wisconsin) or just Wisconsin?