State tax filing

If you are a "resident" of California for 2011, you owe income tax on your income even if it was earned out of state.  You are a CA resident if you are "domiciled" there, even if you are temporarily out of state.  See these links,

https://www.ftb.ca.gov/forms/2015/15_1031.pdf

https://www.ftb.ca.gov/individuals/fileRtn/Nonresidents_PartYear_Residents.shtml

You will need to reply to the letter with proof that you were not "domiciled" in California for any part of 2011.  If, according to their rules, you were domiciled in California, whether for part or all of the year,, you unfortunately will owe them a part-year or full-year tax return.  You should, however, be able to take a credit for any 2011 tax you paid in another state, which would reduce your CA bill.