Rick Santorum was run out of the Senate on a rail back in Pennsylvania over just this issue (and others, to be honest). But the Democrats bludgeoned his political career to death with the non-resident of the district (State) information, even though he maintained a tiny (virtually unused) home back in PA.
Santorum had, and likely still has lots of issues. His fake Pennsylvania residency while living in a multimillion dollar mansion in Great Falls was just one of them.