Not that I'm aware of. There is no way to expedite either a federal or a state refund.
You can track your state refund by using the info below.
https://ttlc.intuit.com/replies/3300211
If you'd like to contact your state taxing authority, the info below will assist you.
https://ttlc.intuit.com/replies/3302452
*** I am NOT a tax expert. I am a seasoned TurboTax user, and volunteer to provide assistance to TT users. Nothing I post is to be considered TAX ADVICE; I bear no legal liability for responses.***
