There really isn't enough information to provide a COMPLETE answer. For instance, do you live on your own or are you a student whose parents claim your exemption? This can make quite a bit of difference in determining your Taxable Income (and, thus, your Tax).
How much was your income and what type of income was it? Did you "earn" the income or was it unearned (interest income, unemployment compensation, pension, etc.).
Also since the deadline for filing the 2010 return has expired are you asking about the 2010 return or the upcoming 2011 return. The figures for Standard Deduction and Personal Exemption could change when Congress comes back from their Christmas break.
But the basic answer to your question is NOT NECESSARILY. We had several clients that got federal refunds back this past year that ended up owing tax to Oklahoma.
Mike Womack, Sr. Partner Zero Degrees Tax LLP Moore, OK
After filing the 1040 EZ, one is entitled to get a federal refund. Depending on how you filed your returns, the duration it will take to have your refund will vary. If you e-filed the returns, you can check your refund status 7 days after you electronically filed the return. If you mailed in your return, you will need to wait for about 4 to 6 weeks before checking on the status of your refund.