Doing some searching on MI State web site and laws, it appears you have to be in good standing to dissolve, and it appears it takes not filing two annual statements to lose good standing.
I would think you can file for dissolution without filing at least one of the annual filings. Can't hurt to call the LARA office in Lansing to confirm.
From the sites:
"Failure to file the annual statement will result in the company no longer being in good standing after two years..."
http://www.michigan.gov/lara/0,4601,7-154-61343_35413_35429-118513--,00.html
"NOTE: If an LLC is currently not in good standing status, in order to file a dissolution form, the LLC must first restore good standing."
http://www.michigan.gov/lara/0,4601,7-154-61343_35413_35429-118500--,00.html
"MICHIGAN LIMITED LIABILITY COMPANY ACT (EXCERPT)Act 23 of 1993
450.4207a Certificate of good standing.
Sec. 207a.
(1) ...A certificate of good standing issued to a domestic limited liability company shall state that it has been validly organized as a domestic limited liability company, that it is validly in existence under the laws of this state, and that it has satisfied its annual filing obligations.
(2) If a domestic limited liability company or a foreign limited liability company authorized to transact business in this state fails to file an annual statement required by section 207 for 2 consecutive years, the administrator shall notify the company of the consequences of the failure to file under subsection (3).
(3) If a limited liability company does not file all annual statements it has failed to file, and the applicable fees, within 60 days after the administrator's notice under subsection (2) is sent, the limited liability company is not in good standing."
http://www.legislature.mi.gov/(S(3pau5z4owtccs1yidcbjfuxl))/mileg.aspx?page=GetObject&objectname=mcl-450-4207a