You may have several filing requirements depending on the value of the stocks as well as whether or not you continue to hold them in a foreign account.
If the value of the stocks plus any other inherited financial assets exceeds $100,000, you will file Form 3520, described above by @ee-ea. No tax is due with the form, and it is not included in any version of TurboTax. It is mailed separately from your income tax return.
If the assets are now held in your name in an account in India you could be required to file FinCEN 114 (often referred to as "FBAR") to report assets held in foreign bank and investment accounts. This form is required if the aggregate balance of your assets held in foreign accounts exceeds $10,000 on any day of the year. This form is also not part of TurboTax and can be filed HERE. You will report the highest balance held in each of your foreign accounts at this site, but you do not need to report each stock holding on this report.
Assuming you live within the US, you could also be required to file Form 8398, which is included in TurboTax. US persons living within the US file this form to report assets that are $50,000 or more on the last day of the tax year or $75,000 at any time during the year. These amounts are doubled if you are married and file a joint return with your spouse. (For taxpayers living abroad, these amounts are $200,000 or $300,00 for an individual and $400,000 or $600,000 for a jointly filed return.)
Finally, for the basis of the stocks, you will use the value on the date of death of the parent from whom you inherited the assets. You won't report that basis on any of the forms described above, but you will report it on Schedule D when you sell the stocks to realize your capital gain or loss.
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