Yes, you would need to file a tax return and the estate is liable for the tax, not you personally. Below are several helpful links explaining what happens tax-wise after a parent's death.
Certain estate property is exempt from income tax levies. This includes the proceeds of life insurance policies, workers' comp and unemployment benefits, and a limited amount of household goods, clothing, tools, books, furniture and real property. If an estate has insufficient non-exempt assets, then the administrator can negotiate with the IRS to reduce the lien. If, however, the administrator transfers assets to heirs without paying tax liabilities, then the IRS (and state tax agencies) will come after the administrator, personally, for the back taxes.
http://finance.zacks.com/happens-federal-income-tax-debt-person-owes-dies-6209.html
http://moneyning.com/money-management/heirs-responsibilities-after-a-death/
http://money.cnn.com/2014/06/19/pf/inherited-debt-adult-children/
https://www.irs.com/articles/death-tax-forms
