It sounds like you owed money on your original return, but when you prepared your amended return, the amended state return shows no balance due. If that is correct, it sounds like the changes made on your federal return did not change the tax due on your state return. I recommend reviewing your original return to the amended return to make sure the changes are carried forward onto your state return. If they are and the total tax is unchanged, then you would not need to amend your state return as there is no change to your overall state tax liability.
Please also see do I need to amend my return and how do I amend my state tax return for additional guidance.