Bloomberg has not officially said whether he will run in the 2020 race, but has acknowledged he is considering a bid and qualified on Friday for the Alabama ballot. Each U.S. state conducts separate qualifying processes.
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Tuesday is the last day for candidates to qualify to be on the presidential primary ballot in Arkansas.
Michael Bloomberg, weighing presidential bid, appears in Arkansas to enter ballot
You could check out your state's election laws.
This is one of the great things about being a Republic, each state's citizens have the ability to make their own state's laws.
That is why some states have stricter accommodation laws than some other states. Each state must meet the federal accommodation laws standard but can be stricter. The same with gun laws, etc.
The federal government, as far as I know, doesn't have any laws effecting election ballots in each state.
That may be why the federal judge said "likely" because he doesn't know if it is unconstitutional, there isn't any federal laws for him to turn to.