TurboTax doesn't get any updates on the status of your refund after the return is accepted.

If I understand you correctly, you have checked on the status of your Louisiana refund on their website and it shows that it was processed on January 27. Did it also say that the refund was issued?

At this point, contacting the Louisiana Department of Revenue is your only option.

Click here for contact information.

No. I have not received my Louisiana state tax return still. Will not use you guys again!

If you filed a Louisiana return and indicated that your refund be direct deposit and you gave TurboTax the bank routing number and your account number, then as Julie said above, you need to contact the State of Louisiana to see if the direct deposit failed (so you can update the info). Or perhaps the direct deposit failed and so the state mailed you the refund check and it got lost in the mail. 

The point is that TurboTax cannot track the progress of your refund because it is in the hands of the state.

Call the state if you want your refund; TurboTax doesn't have it nor has any way to know where it is.