If they choose to have an election they are bound by innumerable laws and decisions...almost all of which are Federal.
However, a state can ALSO determine how a candidate gets on the ballot. A perfect example of this is the Virginia Primary qualification in which a candidate must obtain a minimum number of signature AND a minimum number from every county in the state.
Now, while the US Constitution has only two requirements for POTUS...Natural Born Citizen...and 35 Years of age...I am CONFIDENT the USSC would uphold Georgia's refusal to put ANYONE on the ballot until/unless they sign a release form for the State to obtain a Certified Copy, under threat of law, directly from the jurisdiction of birth.
This to verify the only two requirements to be POTUS.
Even one state would expose the Fraud.
Section 1.......
5: No Person except a natural born Citizen, or a Citizen of the United States, at the time of the Adoption of this Constitution, shall be eligible to the Office of President; neither shall any Person be eligible to that Office who shall not have attained to the Age of thirty five Years, and been fourteen Years a Resident within the United States.
There are 3 requirements:
1. Natural born citizen.
2. 35 years of age.
3. 14 years a resident.
‘Jurisdiction of birth’? This could very interesting in Obama’s situation as there is a bit of controversy as to his place of birth. Granted that Obama might have a truly valid birth certificate cached in Hawaii there might still be questions about Hawaii allowing birth reports to be filed on anyone within a year of birth. Hawaii must be the most rogue state to have ever been admitted into the Union.