I received my federal refund direct deposit last week. I have not received my Maine state refund yet. How long does it usually take?

It varies. The states normally take longer than your Federal refund because it is based on your federal return. 

However, once processed by your state, you can look up your refund status and whether or not a check will be mailed or direct deposited by selecting your state in the TurboTax FAQ below:

https://ttlc.intuit.com/replies/3300211