State tax filing

It depends.

Are the federal amounts the same?

If so, does the new 1099-MISC form show that is was corrected?

You would find this box on the top of the form.

As long as the form has the Payer's TIN and is marked as being Corrected, you would be fine.

If however, the payer's TIN has changed, you will need to contact the client and let them know they have reported your income twice to the IRS. 

They should take the appropriate steps to correct their filing to ensure you are only issued a 1099-MISC for the income you actually receive and that any other forms issued erroneously are corrected.