Mich. Comp. Laws § 750 regulates what is often known as eavesdropping or wiretapping. The core prohibition is §539c, which says
Any person who is present or who is not present during a private
conversation and who wilfully uses any device to eavesdrop upon the
conversation without the consent of all parties thereto, or who
knowingly aids, employs or procures another person to do the same in
violation of this section, is guilty of a felony
An open faculty meeting is by law not a private conversation (however, a closed meeting is). Per the Open Meetings Act, "the faculty" constitute a public body
(a state "committee, subcommittee, authority, or council", empowered by the constitution and statute to perform a governmental function). §15.263 directly says "yes you may":
All meetings of a public body shall be open to the public and shall be
held in a place available to the general public. All persons shall be
permitted to attend any meeting except as otherwise provided in this
act. The right of a person to attend a meeting of a public body
includes the right to tape-record, to videotape, to broadcast live
on radio, and to telecast live on television the proceedings
of a public body at a public meeting. The exercise of this
right does not depend on the prior approval of the public
body.
A closed session can be called for by 2/3 vote for certain purposes (real estate purchase) and are automatically closed for certain others (actions against an employee, disciplining a student if the student requests...).
It does not follow that the chair or all faculty members know or correctly interpret the law, so you may be denied a legal right. One unsatisfactory remedy would be to sue the university for resulting damages, which would put university counsel in the position of having to defend the university's actions (i.e. what the employees did). It is possible that there already exists an official university document regarding the public meetings act which would resolve the matter. Or, the university attorney's office might provide instructive guidance, but it is equally likely that they will refuse to respond if the request does not come from the department chair or other empowered administrator, such as the dean. Unfortunately it is not a statutory slam-dunk that a faculty meeting is a meeting of a public body. Case law has centered around the Board of Regents, who do nothing but run the university, and I can't find any case law addressing the matter of the faculty being a "public body". So authoritative persuasion from above may be required.