Do I need to file form 1065 in Michigan? My wife and I started an LLC in 2019. This business was dissolved in January 2020. How can I notify the IRS that it is dissolved?

It depends.  If your wife was the only member of the LLC, and did not elect to be treated as a corporation for tax purposes, she "defaults" to "disregarded entity" status and reports her 2019 income and expense on Schedule C as if she was a sole proprietor.  If the LLC has multiple members, it "defaults" to a partnership and must file a Form 1065 partnership return.

You indicate on the applicable form (Schedule C or Form 1065) when it is the final year for a business.

For Michigan, the LLC is not required to file a separate return as long as the income is reported on your individual tax return via Schedule C or Schedule K-1.

See this IRS web site for more information on LLC business entities.