That depends. Do you live in a community property state? The IRS states the following with regard to community property:
If your domicile is in a community property state during any part of your tax year, you may have community income. Your state law determines whether your income is separate or community income. If you and your spouse file separate returns, you must report half of any income described by state law as community income and all of your separate income, and your spouse must report the other half of any community income plus all of his or her separate income. Each of you can claim credit for half the income tax withheld from community income.
Have you received the 1099-INT? While your bank account was in your joint names, generally 1099-INTs will be issued to the primary account owner, and therefore, the primary account owner may pay the tax.
Additionally, the IRS will likely not follow whatever agreements you may have/had with your ex spouse or whatever your divorce decree includes with regard to tax liabilities.
@sam_ds75
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