Yes, this is normal. Federal (IRS) and State (each individual state) is processed separately. Each state processes differently and at different times so the time frame can vary. Also, keep in mind some tax returns need extra review for accuracy, completeness and to protect taxpayers from fraud and identity theft. Extra processing time may be necessary. 

If you're concerned, contact your state department of revenue at the link given below. Click on your state for contact information:

How do I contact my state Department of Revenue? 

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