Does turbo tax automatically file amended state returns

[DoninGA]

No.  Only you can complete, sign, date and mail the state amended tax return to the state.

See this TurboTax support FAQ for amending a state tax return - https://ttlc.intuit.com/community/amending/help/i-need-to-amend-my-state-return/01/26510

[Critter-3]

TT doesn't send anything automatically ... it is a DIY program so you must DIY.