No. The state and Federal refunds come from 2 different taxing agencies. There's no way to know which one comes first. Sometimes the state comes before the Federal, and vice versa. Some states can take a long time. Your state website may have a FAQ telling about how long it takes in your state. You can go there and monitor your state refund using this FAQ:
NOTE: Also, if you efiled, be sure your state return was successfully efiled and accepted. You can check at the Tax Home of your Online TurboTax account.