Depending on what state you are in, it's very normal if your return still shows in accepted or pending status for an extended period of time after your federal return has been accepted. The processing times for each state can vary tremendously.
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How do I track my state refund? select your state and most states have some type of note on their refund tracking page that states how long processing may take. If there is no note there, no need to be alarmed. Just keep an eye out on there site for updates.
NOTE: If you contact the state or try look up your refund status while your return is still pending, don't be surprised if they tell you "no record found." This is normal; until that state starts reviewing and processing your return, they won't have any record of it.
