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Yes - there is a statute of limitation. Here is the law - http://www.pacode.com/secure/data/061/chapter119/s119.14.html
§ 119.14. Limitations on assessment and collection.
(a) The amount of any tax imposed by this article will be assessed within three years after the return was filed.
§ 119.15. Omission from return.If the taxpayer omits from the income stated in the return of a tax imposed by this article an amount properly includable therein which is in excess of 25% of the income so stated, the tax may be assessed, or a proceeding in court for the collection of such tax may be begun without assessment, at any time within 6 years after the return was filed.
However if the tax return was not filled - the statute of limitation would not apply.
So you need to request from PA DOR a copy of your 1988 tax return.
If you would not be provide a proof that your tax return was filled - you might be held liable for the tax.
Let me know if you need any help.