There is nothing in the Constitution that says they can’t be from the same state.
Technically, you are right.
But in practical terms one of the candidates would forfeit the electoral votes of their own state.
Article 12 says:
The Electors shall meet in their respective states, and vote by ballot for President and Vice-President, one of whom, at least, shall not be an inhabitant of the same state with themselves ...
So if two Georgians ran for President and Vice President on the same ticket, Georgia's electors couldn't vote for both of them.
In theory, you could get Cain and Biden as President and Vice President.
That, and the desire to avoid the appearance that one state was dominating the others, is why Bush and Cheney ran from Texas and Wyoming, even though Cheney had been living more in Texas than in Wyoming in the years before the election.
AMENDMENT XII
Passed by Congress December 9, 1803. Ratified June 15, 1804. Note: A portion of Article II, section 1 of the Constitution was superseded by the 12th amendment.
The Electors shall meet in their respective states and vote by ballot for President and Vice-President, one of whom, at least, shall not be an inhabitant of the same state with themselves; they shall name in their ballots the person voted for as President, and in distinct ballots the person voted for as Vice-President ...