Washtenaw County Death and Marriage Records
Searchable death records from 1960 to the present and searchable marriage records from 1965 to the present can be found on the Washtenaw County Clerk/Register's Office website.
The Ann Arbor District Library (Second Floor of the Downtown Library) has the Ann Arbor News on microfilm. You can search for an obituary using the date of the death as a starting date. If there is an obituary, you will usually find it within the first two or three days after the date of death.
The Ann Arbor News keeps obituaries online for the past 180 days.