If you already completed (or are mostly finished with) your 2018 state
return in TurboTax Online, go back into your state and look for a Need more time to file?
or similar extension question or option, usually towards the end of the
interview (step through your state again from the beginning if you
didn't find it). Then follow the onscreen instructions in TurboTax.
Otherwise, if you haven't (or you just) started your 2018 state return, see below for alternative instructions for Maine:
Maine (ME) automatically grants a 6-month extension to October 15. If you owe them taxes, submit payment by April 15 to avoid penalties. You can either include a check with Form 1040EXT-ME or pay online at their EZ Pay site.