I moved from NC to CA and owned a first home(resident) in CA. Can the mortagage interest be deducted from taxable income in both CA and NC state income taxes?

The way it works is that you report the full mortgage interest on your Federal return.  Since you lived in both North Carolina and California, you will be filing Part-Year returns for each of those states.  The following article explains how TurboTax will apportions your income and deductions to each state. Multiple States Returns

Yes part year is understood but my question is if the mortagage interest i paid for property owned in CA can be deducted from NC state taxable income as well or not?