No, it is not tax exempt. You were given a home that had a certain cost basis (the amount your parents originally paid for the home, plus any improvements they paid for). The gift of that cost basis is not taxable. But anything you get that is over the cost basis is taxable capital gains to you. If you don't know your parents cost basis, you need to find out. (If you can't ask your parents, the county will have records of what they paid, and may have records of building permits for improvements.). If you can't prove your cost basis and you are audited, the IRS does not have to give you any basis you can't prove and if they determine your cost basis is zero, the entire sales proceeds will be deemed capital gains. (There are certain adjustments allowed to cost basis, see publication 523.)
https://www.irs.gov/forms-pubs/about-publication-523
Assuming that you and your parents combined owned the home more than 1 year, this is a long term capital gains which is taxed at a lower rate (15% for most people, 20% for some high income taxpayers.)
On your federal tax return, enter the transaction under sale of stock, bonds and other property, use "other property" (not "my home" because that section contains items that only apply to a home you lived in as your main home). You will be asked for the date acquired, how acquired, cost basis, date of sale, proceeds and selling expenses.
If you are preparing 2 state income tax returns, I assume one as resident and one as non-resident, you don't say where you live. If you live in PA, then when preparing the NY return, you will be asked to allocate your income to the state where it was earned, be sure to allocate the sale of the home 100% to PA. If you live in NY, the gains are taxable in PA (because the property is located there) and also taxed in NY (because if you are an NY resident, all your worldwide income is taxed in NY) but NY will give you a credit for PA taxes you pay on the sale.
Also beware, if you have a lump sum of income, you need to pay estimated taxes and you probably need to include form 2210 with your tax return. Suppose you sell the home on August 15 and have a gain of $100,000. The tax (depending on your other income) will be $15,000 or $20,000. The IRS default position is that income is earned evenly over the year, meaning that you owed a payment of $3750 by April 15, $3750 by June 15, $3750 by September 15, and $3750 by January 15, 2024. Even if you pay the entire estimated tax when you sell the home, those amounts from April and June will be deemed overdue and subject to a penalty plus interest. You can avoid this by including form 2210 with your tax return (calculating estimated penalties) and using the Annualized Income method, which is a way of showing the IRS that your income was uneven during the year, and that you paid the required amount due for each quarter.
If you sell the house before August 31, you need to make an estimated payment of 15% of the gains by September 15. If you sell after September 1, the estimated payment is due January 15, 2024. If your income is over the limits show on this web page, you should probably make a 20% payment.
https://www.irs.gov/taxtopics/tc409
If you overpay the estimate, you will get the extra back as part of your tax refund.
Lastly, let me note some special circumstances.
If your parents gave you the house as part of their estate planning, on the condition that they could live in the house until they died, you might have an implied life estate, meaning your cost basis is stepped up to the fair market value on the date the last survivor died. Or, if you were given part of the house as a joint tenant with right of survivorship (JTWROS) you might have a stepped up basis. This would greatly reduce your capital gains. You would need to see an attorney to review your situation to determine if you qualify for this.
