Thanks for the extra clarification, hdwatson. As SuperUser @Lisa995 correctly observed and noted (credit to her for doing so), Form 966 is used to report a corporate dissolution to the IRS (in other words, a Form 1120 type filer). This is not what's needed for the wrapping up and dissolution of a Limited Partnership.
Assuming that you've been filing Form 1065, and associated Schedule K-1s, for your partnership, it is totally sufficient -- and indeed the correct course of action -- to simply mark on your final year 1065 that this is, indeed, your last year of operation. The final K-1s will report the flow-through partnership income to the respective partners (both limited and general, if applicable).
There may be some other legal formalities that probably should be followed at the state level when dissolving a limited partnership, but I am not a lawyer and we are not supposed to provide that sort of advice here anyway (company policy). Nevertheless, I would respectfully recommend speaking to a local attorney, if only very briefly, to learn if there is something else that you should do, such as notifying your state's business recording section, bureau, department, or similar.
Bottom line for tax purposes, however, is that you need do nothing for the IRS other than complete your last 1065, K-1s, or such . . . marking them with the "final" checkbox (just as you seem to have suggested in your original post).
I hope all this information is helpful, and thanks for asking this important question! Good luck!
Regards
