It depends but if you have net rental income on this MI located rental property, you will need to report this MI sourced income on both an MI nonresident state income tax return and your CA resident state income tax return. If you have net rental losses then no MI nonresident filing requirement is necessary (although you will still need to report this rental property on your CA resident state income tax return).
If you are a permanent resident of CA and have MI sourced net rental income only (not a net loss), then you will need to file an MI nonresident state income tax return (for your MI source net rental income only). You will also need to file a CA resident state tax return (for all income from all sources including MI rental income/losses). You will get a state income tax credit in CA for any MI state income taxes that you paid on your nonresident MI state income tax return.
You will want to work on your nonresident MI state income tax return first. You will then take a tax credit from your nonresident MI state income taxes on your resident CA state income tax return. (Please note that you will only get a tax credit for your MI state income taxes up to the amount of CA state income taxes that would have been paid if the income was earned in CA). The credit for taxes paid to another state section will be at the end of your residence state's interview process.
Just follow the TurboTax guide when working on your states (remembering to do your nonresident state return first) and TurboTax will do all the calculations and credits to your resident states return
Here is additional information about filing in multiple states (select "see more answer" to view the entire attachment)
https://ttlc.intuit.com/replies/3300797