After you finish reading my answer, you should feel comfortable in advising California FTB that their claim is unwarranted and not legal under the Servicemember's Civil Relief Act(I have enclosed the website for that Act).
No Statute of Limitations Exists unless a California tax return was filed.
1. The issue here is not a "statute of limitations" which starts running at the time you file a tax return. Since no return was filed by you for California taxes originally, there is no SOL to be considered.
To Be A California Resident:
2. If you abandoned your Tennessee legal residence (domicile) and established a legal residence in California, you would have been classified as a California resident.
A Tennessee legal resident (domiciliary) who enters the armed forces remains a Tennessee legal resident unless positive action is taken to abandon Tennessee residency and establish legal residence in California.
Changing legal residence requires: (1) physical presence in the new locality, (2) an intent to remain there permanently or indefinitely, and (3) an intent to abandon the old legal residence. Actions which express intent may include, but are not limited to: (1) changing legal documents, such as a will or insurance policies, to reflect the new legal residence, (2) changing home of record upon reenlistment, (3) registering to vote in the new locality, (4) paying state taxes in the new locality, (5) applying for a driver's license in the new state of residence and relinquishing the Tennessee driver's license, (6) registering a car in the new state of residence and relinquishing Tennessee car registration, (7) purchasing a home in the new state of residence and selling a Tennessee home, and (8) consistently using the new permanent address on all appropriate records and correspondence. Moving from one duty station to another does not by itself constitute a change of legal residence.
Under the Federal Servicemembers Civil Relief Act, as a Tennessee resident in the armed forces you cannot be taxed on military pay by any other state. However, a Tennessee resident can be taxed as a nonresident by another state on income, other than military pay, earned from employment or property in that state. In such a case, a tax credit would usually be allowed by Tennessee.
Quoting from the Servicemember's Civil Relief Act Guide:
"Military pay is not considered income from services performed or from sources within a tax jurisdiction if the member is not already a resident or domicile of the jurisdiction in which he located pursuant to military orders." http://www.uscg.mil/legal/la/topics/sscra/sscra_guide.htm#collection_tax (please review this guide at your leisure or advise the state of California to read it and drop their claim based on this law.
I do think that this will resolve your issue.
Don't ignore the California notice. Make sure to inform them of the Relief Act that protects you form taxation by jurisdictions other than your domicile...your Tennessee.
Please remember to click the Green ACCEPT button and leave a little FEEDBACK.
I have a feeling you'll be getting a California refund on your wife's income;
Since you do not have to report military pay for California tax purposes, the only taxable income you would report on a California tax return is your wife's. As it is probably under the lower limit for taxation, you would be getting a refund of any withholding. That state income tax withholding should be on your wife's w-2....and that whole amount is very probably a refund.
As unlikely as it seems to me, if she did owe a bit of California tax, that amount would be a tax credit on your Tennessee tax return anyway, so you would not be out a cent.
File California and get your refund...just remember that your military pay is not a part of that return....just your wife's income earned in California. I'm attaching California returns here so that you can think about it.