Work and lived in Michigan, moved to Indiana mid-year, who/where do I file state with?

You would file a part-year resident return for Michigan and a part-year resident return for Indiana for the time lived in each state. 

Michigan and Indiana have reciprocal agreements. A reciprocal agreement, also called reciprocity, is an agreement between two states that allows residents of one state to request exemption from tax withholding in the other (reciprocal) state. Typically, this can save you the trouble of having to file multiple state returns. However, since you moved mid-year, you will still have to file two part-year returns. 

If your employer has withheld taxes for the work state (Michigan) instead of the resident state (Indiana), you'll have to file for a refund from your work state. You'll still file your resident return that also includes that income and pay tax on it. You will pay taxes to Michigan for the time lived in Michigan and taxes to Indiana for the time lived in Indiana. 

You also need to file form MI-47, Employee's Michigan Withholding Exemption Certificate, with your employer so they can withhold Indiana tax from your pay, rather than Michigan tax.