The states do have a requirement that candidates must live in that state to run for office. Candidates are getting around it by using local addresses as their home address. Kristof's case was a perfect example. He tried to use a local address as his "home" address despite the fact that he lives in NYC. He didn't get away with it because he is so well known and it is well known where he actually lives.

As for the Senate, it's a Constitutional requirement that candidates for the US Senate must reside in the state that they represent. Kristof was running for governor which is a state matter. Each state has their own requirements for how long you must be resident to run for governor.