In TurboTax Business, you'll find this question under About Your Business. Continue from the Business summary page and check the radio button for "Is filing its final return..." The next page asks you about a short-year return (see screenshot below - click to enlarge).
For the SMLLC, you also indicate that the business was sold or disposed of under the business profile in TurboTax Home & Business. Because your ownership changed from a SMLLC to a multi-member partnership, your former LLC ended on the date the new partnership was formed. TurboTax doesn't ask for the date the SMLLC ended, since this isn't reported to the IRS.
The new multi-member partnership began on the date you admitted the new member.
Note that if the new member purchased a part of your membership interest, then you will report a gain or loss on the sale of the assets in the SMLLC when it dissolves. (Your sales price is the amount you received for the portion taken by the new member.) The partnership receives a carryover basis and holding period for the assets you contributed that is same as the SMLLC. The new member's holding period begins the day after his/her purchase of that portion of your interest.
But if the new member contributed cash in exchange for an interest in the new partnership, you would not report a gain or loss on the dissolution of the SMLLC. Instead, you have a basis in the new partnership that is equal to the assets you contributed. And the new member's basis is equal to the cash that was contributed.
If the tax and legal issues regarding the formation of the new partnership are not clear to you, consider consulting a local tax professional who would be more familiar with your personal tax situation.
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