Since you posted these events as occurring in the future, this seems to me to be a hypothetical situation rather than a real one, making me think this may be more of a homework problem or something similar. Normally we don’t do homework here.

But I’ll give you some information to get started. Under Colorado income tax law, a person is resident in Colorado if his or her domicile in that state. Your domicile is your place of permanent residence; the place at which you have the most ties and the place to which you intend to return after being away, even if that absence is for a long period of time. Under your facts, the family was apparently domiciled in Colorado through at least 12/24/16. You say that they then sever “all ties to the property” as of that date, which doesn’t tell me a whole lot. Selling a home does not itself mean your domicile in the state has ended. Does the person have an intent to return to Colorado once the foreign work assignment is over? If the answer is yes, then the person is likely still domiciled in the state. Factors that the state will look at as evidence of intent to return include things like: is the person still registered to vote in the state, does he or she still has a driver’s license and/or other licenses in the state, still has membership in a church or other organizations in the state, does the person maintain a home in the state, have other assets in the state, is the person’s permanent employment location in the state and thus where the person will return after the assignment, etc.

Unless the person cuts off all significant ties to the state, the state may assert the person’s domicile is still Colorado, particularly if the assignment is known to be of limited duration and the person will return to the U.S. afterwards. If the person is a resident of the state (domiciled there) then all of his income is subject to tax by the state. If the person does end domicile in Colorado, then only Colorado source income will be subject to tax in that state thereafter. Note that it is not necessarily the location of the person making the payment of income that determines the source. That varies depending on the type of income. While the employer paying the person may be in Colorado, income for personal services performed is generally sourced where the actual services are performed, not where the employer paying the wage or salary is located.

The stay in Ohio is clearly just temporary while in transit to the foreign country and never becomes the domicile of the taxpayer here. Simply having a mail drop address in the state does not establish residency or domicile there.

Finally, for federal income tax purposes, if you are a citizen or permanent resident (i.e. “green card” holder) of the U.S. then the federal government taxes all of your income no matter where in the entire universe you happen to live and no matter where in the universe your income is sourced. You could be living on a colony on Mars and if you are a citizen of the U.S. you will still pay tax to the U.S. on on your income (though you do get a credit for foreign income tax paid on that income). There are a number of special rules that apply to persons who give up citizenship/permanent residents and leave the country (ex-pats) that ensure they do not avoid tax when they leave on income that accrued while in the U.S.