Conversion from S-Corp to LLC Federal EIN Change

Was this entity originally an LLC that "elected to be treated as an S-Corp"

Short version: if the LLC will continue to be taxed as a corporation (C or S), no new EIN. If it will be taxed as a partnership or disregarded entity, you need a new EIN (and have a taxable event). 

https://www.irs.gov/businesses/small-businesses-self-employed/do-you-need-a-new-ein

Corporations

You will be required to obtain a new EIN if any of the following statements are true.

• A corporation receives a new charter from the secretary of state.
• You are a subsidiary of a corporation using the parent's EIN or you become a subsidiary of a corporation.
• You change to a partnership or a sole proprietorship.
• A new corporation is created after a statutory merger.

You will not be required to obtain a new EIN if any of the following statements are true.

• You are a division of a corporation.
• The surviving corporation uses the existing EIN after a corporate merger.
• A corporation declares bankruptcy.
• The corporate name or location changes.
• A corporation chooses to be taxed as an S corporation.
• Reorganization of a corporation changes only the identity or place.
• Conversion at the state level with business structure remaining unchanged.