As a pass-through entity, the LLC is not required to pay state income tax. Tax paid under the LLC's tax id will be credited to the owners of the LLC. Depending on the state, you may need to include the tax payment on the K-1 from the LLC.
When you complete the state income tax interview for your personal return, look for questions under the K-1 topic that relate to tax paid on your behalf by the LLC.
Note that the LLC may need to pay franchise tax to the state, which is not the same thing.
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