I'm looking to register everything I own in Michigan. I work and live in New York. How would that affect my tax returns at the end of the year as well as income taxes?
If you work and live in New York, you are a New York resident, not a Michigan resident.
What do you mean by "register everything I own"? It doesn't sound like something that would change your residency status. Your residence is basically determined by where you live.
Here is a link to the definition of a resident for New York income tax purposes.
Note that one of the ways that you could be considered a New York resident is that "you maintain a permanent place of abode in New York State for substantially all of the taxable year and spend 184 days or more in New York State during the taxable year." If you live in New York, you most likely meet that definition.
The Michigan income tax instructions simply say "You are a Michigan resident if Michigan is your permanent home."
Note that neither state's definition of a resident is based on where anything is "registered." Also note that, because each state defines a resident differently, it is possible to be considered a resident of two states at the same time. When that happens, you might have to file resident tax returns in both states.
If your residency status is not clear, you should probably consult a tax professional who specializes in multi-state taxation.
The general rule is: your report all your income on your home state return, even the income earned out of state. You file a non-resident state return for the state you worked in and pay tax to that state. Your home state will give you a credit, or partial credit, for what you paid the non-resident state.
But, as the other reply indicates, which state is your resident state depends on the details. From what you describe (living & working in New York full time), you are a NY resident. Having a 2nd home in MI doesn't give you the "option" of declaring MI your tax home.