If my mother passed away in November 2013, can I file her taxes both for State and Federal?

Did your mother leave a will? Does she have an estate (that is did she leave any assets where there was no beneficiary designated such as bank accounts automobiles investment accounts and the like). If she did leave a will and you are the personal representative you can file her final tax return but remember that when you file that return as her personal representative you are personally liable for the taxes that she owes.you need to check and see what types of legal documents if any she left for you file her returns. Did she leave a will is a mentioned before or was there a trust, or had somebody been designated as her agent under a power of attorney. While that power of attorney expires on the time of her death the person designated as her agent may have information regarding her assets and what she wanted done with her final taxes etc.

Yes. Note that income and expenses from January 1 through the date of death go on her return. After her death any further income or expense is retorted by her estate, trust or beneficiaries.

Your mother's executor must file her final tax return. At the top of the return, mark "Final" and "Date of Death xx xx 2013".

The personal representative normally files the final taxes, and either pays the tax, or deposits the refund into the estate for distribution. See an attorney!