The short answer to the question is: yes, no, and depends.
Debts arising from income taxes can be classified as secured, priority and unsecured debts. The classification of the debt determines its dischargeability. That is, secured debts and priority debts are non-dischargeable. Unsecured debts are dischargeable.
The factor that determines how an income tax debt is classified depends on when an income tax return is filed or whether the taxing authority has filed a tax lien. If a tax lien has been filed by then the debt becomes a secured debt and is non - dischargeable. Additionally, a tax debt that arises from an unfiled tax return, is non - dischargeable. Likewise, a tax debt arising from a tax return that was filed both late and within two (2) years prior to the filing of a bankruptcy petition (the date that the bankruptcy is commenced) is not dischargable. (See 11 U.S.C. 523(a)(1)).
Nevertheless, Income tax debts are dischargeable if the tax became due three (3) years or more before the petition date and the associated tax return was filed more than two (2) years before the petition date and the taxes were assessed at lease two hundred and forty (240) days before the petition date are dischargeable. (See 11 U.S.C. 507(a)(8) and 523(a)(1)).
So, an example of a dischargeable tax debt would be a taxes owed by a Debtor who filed a timely tax return on or before April 15, 2012 for tax year 2011. In this scenario, if the Debtor filed a bankruptcy petition on or after April 16, 2015, the debt would be dischargeable. Likewise, if the same Debtor filed a late tax return on April 15, 2013 the debt would still be dischargeable because the tax return was filed more than two (2) years before the petition date and at least three (3) years after the tax became due.
In the same example, suppose the Debtor made an error in the tax return and the tax authority assessed additional taxes. If the assessment was more than two hundred and forty days before the petition date then the taxes are still dischargeable!!