LLC doesn't really mean anything to the IRS. Your business filing requirements depend on how your LLC is treated for tax purposes. If you have a single-member LLC, then it's not considered a separate business entity by the IRS, you'd file a Schedule C like any sole-proprietor, and you only have a Schedule C filing obligation if your income is over $400 for the year (total from all businesses if you have multiple sole-proprietorships).
If you have partners in your LLC, then it's treated by the IRS like any other partnership, you only have to file a 1065 if you had any income or expenses for the year.
The caveat to both of the above is if you elected to have your LLC treated as a corporation then you must file a tax return for the corporation.
Here's a handy article from LegalZoom:
Do I Need to File a Tax Return for an LLC With No Activity?
And this person asked a nearly identical question to yours over on the TurboTax foruum:
I started a LLC in 2016 that did not generate any income nor expenses. The LLC is still active is this something I need to add on my taxes?
Edit: It occurred to me that NY may have its own requirement for filing. With no income to show, you do not have to file Form IT-204-LL (LLC Filing Fee), so that saves you $25 (much higher annual fee if you elect to be treated as a corporation in the future, make sure to weigh that into your decision). I didn't see anything that suggested you'd have to file anything for your LLC in NY without income/losses.