Once your return is filed, TurboTax has no control over the processing of your return or the release of your refund.
Due to PATH Act, the IRS holds refunds for EITC/ACTC customers until March 3.
Here are a couple FAQs to track your refund:
When will I get my federal tax refund?
How do I track my state refund?
Why does Where's My Refund say "approved" but TurboTax still says "accepted"?
That's not what I asked I asked if I e-file my state return on a Saturday and that Monday was a holiday will it be sent to the maine revenue services that day or will it take a couple days before they receive it
When a tax return is efiled, or transmitted, it doesn't go to a person, it goes into a computerized processing system.
Only if there is something that triggers a review, (or sometimes a return will be pulled for a random check) the return goes through this process until approved.
To answer your question, the holiday should have made no impact on the return being sent to the state's computer system.
The return is transmitted as soon as the receiving end accepts it. These processing centers run 24/7.