Purchasing a house is usually considered establishing residency. If those are your facts, it is much safer to say that you are a North Carolina resident, and you probably can claim such for the entire year based on the sales date of the CA home. That would make any California income nonresident income (which, you would be filing a California Nonresident return anyways with your situation). What you will need to determine is how much of your California income was earned physically working in California. Whatever that figure was will determine your California tax. Whatever California taxes the California income may be claimed as a credit towards North Carolina state tax. North Carolina will tax all of your income regardless of where it was made.
This would be the easiest and safest way to file based on the facts provided. Having a place to stay in CA while working there does not make you a resident there. This is supported by your home sale. It may or may not result in more overall tax, but you will have less complications in preparing or substantiating the returns if need be.
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