Troy and Aubrnhills Michigan do not have city tax.
According to the State of Michigan:
For 2016 the following Michigan cities levy an income tax of 1% on residents and 0.5% on nonresidents.
Albion, Battle Creek, Big Rapids, Flint, Grayling, Hamtramck, Hudson, Ionia, Jackson, Lansing, Lapeer, Muskegon, Muskegon Heights, Pontiac, Port Huron, Portland, Springfield and Walker.
Detroit 2.4%
Grand Rapids 1.5%
Highland Park 2%
Saginaw 1.5%