More than likely, yes, under the current law, but it should be considered carefully because it ultimately depends on the factual context of the situation, and there also will be practical reasons to consider. The statute governing these types of circumstances (whether an individual can hold positions in two different public offices) is Michigan’s Incompatible Offices Act. See MCL §15.181. In most cases, this statute is applied to situations dealing with two elected or appointed positions. However, this question poses a circumstance dealing with an office manager, which is construed as a township employee of one of the townships. The statute has been construed to include positions of that nature. MCL §15.181(d).
Understanding that the act still applies to township employees, a three-part test has been established under this Act to determine whether two public offices are “incompatible.” If one position: (1) subordinates another position; (2) supervises another position; or (3) causes a breach of duty of public offices, then holding those two positions constitutes as incompatible offices, and the individual must step down from one of the positions to avoid the issue of incompatibility and non-compliance with the statute. MCL §15.181(b).
Based off the question submitted, parts one (1) and two (2) of the test more than likely would not apply. The Treasurer position would not subordinate or supervise the Office Manager position, and the same can be said vice versa. Therefore, the breach of duty should be analyzed. The Supreme Court of Michigan addresses the breach of duty issue in Macomb County Prosecuting Attorney v. Murphy, where the Court considered the incompatibility of a defendant who was a tax coordinator in a county treasurer's office and was an elected trustee for a separate township. The Court found that the office positions were not incompatible because there was only a potential breach of duty, which is insufficient. In order for a breach to occur, there must be an actual breach of duty when performing the obligations of the office positions.
Here, as described as Office Manager, it can more than likely be said that this position is performing administrative and managerial duties and no breach of duty of also holding the public office of township trustee exists. The positions can more than likely be held at the same time.