Here is the 24th Amendment to the Constitution of the United States:
Passed by Congress August 27, 1962. Ratified January 23, 1964.
The right of citizens of the United States to vote in any primary or other election for President or Vice President, for electors for President or Vice President, or for Senator or Representative in Congress, shall not be denied or abridged by the United States or any State by reason of failure to pay poll tax or other tax.
In the Jim Crow days, charging people for the right to vote was common. This amendment put an end to that for federal offices. To the best of my knowledge, no state was willing to have a separate election for state offices which could have been subject to a poll tax. Do you know differently?