Last year, I was a non-resident and did not have the normal standard deduction (available for residents), so I itemized my deductions using the State and local taxes I paid.

This year, I am now a resident. Is my last year's STATE TAX REFUND(that I got for overpaying in 2013) taxable for 2014 Federal tax purposes?

Yes, at least in part, because the state and local taxes were deductions that reduced your taxable income.

The state tax refund thus must become income in the following year to prevent people from massively withholding the state income taxes to reduce the federal income tax, then get deductions reimbursed to them in the form of a refund.