No it does not.
That would have been stupid, since the early Fathers who became presidents were from a few states. No where in the constitution does it say that.
Get educated and read it. It has been precedence, and that is all. At no time has the US Supreme Court ever visited it because no one challenged it.
You read the constitution, and you will not find any constitutional law that forbids it, nor any court ruling from SCOTUS ruling on it. PERIOD.
"The Electors shall meet in their respective States, and vote by Ballot for two Persons, of whom one at least shall not be an inhabitant of the same State with themselves..."
The same provision is included in the Twelfth Amendment which modified the procedure for electing the President.
A party could put two persons for the same state on its ticket, but if its electors carried that state, they would be able to vote for only one of the two candidates. If Cheney had not changed his registration, the Texas electors could not have voted for him...so Joe Lieberman would have become Vice President in 2001 (and probably President because the Democrats would then have had an incentive to kill GWB).