In the United States Military, there is a difference between the terms "Home of Record," and "Legal Residence."
"Home of Record" and "Legal Residence" may, or may not be the same address. One's "Home of Record" is the place one was living when they entered the military (or, re-enlisted in the military, if one chooses).
"Home of Record" is used to determine travel entitlements when one separates from the military. It has nothing to do with voting or paying taxes, registering vehicles, nor any of the other priviledges of state residency.
"Home of Record" can only be changed if there is a break in service of more than one day, or to correct an error.
"Legal Residency," or "domicile", on the other hand refers to the place where a military member intends to return to and live after discharge or retirement, and which they consider their "permanent home." Legal residency determines what local (state) tax laws a military member is subject to, and in which local (city, county, state) elections they may vote in.
Because military members may have "legal residence" in one state, but be stationed in a different state, the Servicemembers Civil Relief Act, allows military members to pay taxes, register vehicles, vote, etc., in their "state of legal residence," rather than the state they are stationed in. This can sometimes result in a tax advantage because several states exempt military pay from state taxes.
Does that mean a military member can change their "legal residence" anytime they want, and therefore avoid paying state taxes? Not quite. Under the law, "legal residence" is the place that the military member intends to live after they separate or retire from the military. It's the place that they consider their "permament home."
Depending on their service, and local polcies, an active duty military member can change their "legal residence" by visiting their local base legal office and/or base finance office and completing a DD Form 2058, State of Legal Residence Certificate.
However, the military is required by regulation to ensure that military members are not changing their "legal residence" for the sole purpose of obtaining a tax advantage. Therefore, when changing your "legal residence," military officials at the legal office (or finance office) may require some degree of proof that you consider the new state to be your "permament home."
The easist proof is "physical presence in the state." If you are currently stationed in a state, and wish to make it your permament home, it's generally pretty easy. If you are not currently stationed in the state you wish to make your permament home, and have never been stationed there, it become much harder. Generally, you need a specific address, not just the state in general. You can show your intentions to become a legal resident by registering to vote in the new state, by titling and registering your car in the new state (notifying your old state of the change), by getting a driver's license in the new state, or by preparing a new last will and testament (indicating your new state as your legal residence). Buying real property in the new state will also reinforce your claim.
Unless you can show such clear intentions, the military will probably not allow you to change your "legal residence."
Particular care should be taken to ensure your pay records are up-to-date concerning your state of legal residence. If incorrect, you may wind up paying taxes to the wrong state, or paying taxes and penalties in more than one state. If you have any doubt about your state of legal residence, contact your legal assistance office.
You may also be required to complete a W-4 form to determine the amount of withholding, or exemption from withholding state taxes.