Do I need to use the self employed product if I have an LLC with zero income

It depends. If your business was assigned an EIN before the end of the tax year, you should include Schedule C for this business to avoid an inquiry from the IRS. Once you have an EIN, the IRS expects a return every year. 

But if you don't have an EIN, or if you have never reported this business activity, you are not required to include the LLC on your tax return. If you have reported this activity in the past, you are expected to continue to include the LLC on your return until you close the business, even if you had no income or expenses.

Note that if you filed an S-Corp election, you must file a business tax return (Form 1120-S, available in TurboTax Business).