How do I get custody of Someone living in a different state when her mom goes to jail I am 23 she Is 16?

Ok I live in Ann Arbor Mi and traveled all the way to Peoria Illinois to help this person she was in an extremely abusive household where she was in danger of her life if she stayed she decided to run so I picked her up we made it as far as Grand Rapids Michigan where there was a super bad rainstorm and a cop pulled me over cause I was in passing lane of the freeway (94) too long and there was a really bad rainstorm (to the point where we almost couldn't see) he basically told me he didn't think I should be trying to drive through it so anyways he told me to exit at a gas station, which i did and he followed me, he was very nice and understood what I was trying to do and that I really did care about this person the cop also knew why I wanted her in Ann Arbor too cause there were some racist people where she was at and her town was very conservative another thing I have to deal with the political and social climate of her area and mine as well as a lot of Michigan from what I am finding out is almost completely opposite which is going to way complicate the process here) he really didn't want to take her back to peoria but had no choice as he told me it was the higher ups that made the decision. She told me the cops were very understanding of her situation, and will arrest her mom basically she threatened to beat the *** of an eight year old child tried to pour amonia on her left scars on her etc and the list goes on and on constant verbal abuse she kept her unable to leave the house for three months etc Anyway basically we are in love and have been talking for awhile the cop understood that too but says the law is the law and nothing else can be done. So how do I go about this Michigan law states at 17 and the cop told me and I looked it up she is legally able to be here as an adult and do her thing but I risk it if I go through her state again because the law in her state is 18. Anyways how do I open a case here.