do I have to amend state return due to an employer w2 error?

My employer sent me a w2c indicating the original w2 under reported my state income. However, I already filed my state return. Federal return should not be affected but my state return is. The new calculation indicates I own the state around one thousand. Should I amend my state return immediately or should I wait notice from my state and pay back after received the notice. 

I filed the return with the best of my knowledge at the filing and the error is not on my part. Do I have to file the amendment?
Thanks.