I established my Colorado residency by putting the address of the hotel I was at on my Colorado drivers license. I think I was there for two months in 2006. It may be that the drivers license is the key, because the state determined my residency requirements for hunting purposes based on what my drivers license said, and I gotta think if you can get a resident hunting or fishing license, then you are considered a resident by that state. Considering most state agencies are going to ask for your drivers license to determine your resident eligibility requirements, I would amend my previous recommendation to include getting a state drivers license for your desired state of residence. For that, any address you use in that state for the drivers license application should suffice.

I can say it was almost impossible to convince the state fish and game department I was a resident without a drivers license from that state, and almost automatic with it. It is far too easy these days to get a drivers license from any state, so long as you have a current valid one from another state.
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The ultimate result of shielding men from the effects of folly is to fill the world with fools.
-- Herbert Spencer, English Philosopher (1820-1903)