Yes, you do need
to mail both the Federal and state amended returns when you have made a change
or correction that affects the items originally reported on both your Federal
and state returns
Sometimes the bottom line refund or balance due may not have
changed, but if there is a difference in the numbers that were originally
reported then the amended return should be sent.
For some advice about when to amend your return, take a look
at the TurboTax article below.
https://ttlc.intuit.com/replies/3318732
https://ttlc.intuit.com/replies/3288565