Typically I have found the opposite to be true. I cannot remember a time when I received my state refund first. Perhaps it has to do with the state you filed? I file in Georgia, and it takes longer for me to receive that refund than my federal refund. Either way, I wouldn't be concerned, as TurboTax says it may take up to 3 weeks. Finally, try this website to assist you in tracking your state refund.
https://www.irs.com/articles/check-my-state-tax-refund-status
