Citizenship or ...?

In order to vote at any election you have to declare that you are a U.S. citizen. This is fine for naturalized persons but the native born people in any state would be excluded unless they declare U.S. citizenship over state citizenship. To do so places one in a status of choosing the federal government over the state government.

Is there a procedure to remove oneself from the status of U.S. citizenship while retaining ones state citizenship?

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You cannot do that to my knowledge. But you may want to check with your congress person's staff as well--and/or voting officials.