Whether there are any tax consequences depends on the total assets of the estate, including the CD and any other non-probate assets. The nominated executor should disclose all assets on the petition for probate and on the state tax return if the estate is big enough to require a return to be filed. If you were the joint owner on the CD it is considered a non-probate asset and should pass to you outside the Will. But such assets sometimes lead to disputes, so seek the advice of a probate lawyer in the state where the Will is being probated.
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For a NJ resident decedent there are two possible taxes at death - inheritance and estate (NJ). If the asset passed to you (a child) there is no NJ inheritance tax. However, if mom's assets totaled more than $675K there will be a NJ estate tax. This means someone should be handling her estate affairs. If she had a will that would be the executor, if she did not have a will, it would be an administrator. If the CD was joint with survivorship you are not under an obligation to share the CD however. As the person receiving the asset, you will not have realized any taxable income by receiving the principal amount of the inheritance.
This is not legal advice nor intended to create an attorney-client relationship. The information provided here is informational in nature only. This attorney may not be licensed in the jurisdiction which you have a question about so the answer could be only general in nature. Visit Steve Zelinger's website: http://www.stevenzelinger.com/