Legal Question in Criminal Law in Michigan

Re: how long does the state have to file charges

That depends on the potential charge (which you neglected to tell us about).

The general statute of limitations on criminal charges is 6 years, but some have no limitation.

Aside from that, in very rare circumstances, a charge filed before the statute of limitations is violated can be dismissed by the court. One example is where the defendant is in jail or prison and the prosecutor is on notice about that, and does not charge or bring the defendant to trial for a felony within 6 months. Another example is "pre-indictment delay" where the prosecutor's delay in charging results in improper prejudice to the defendant's ability to muster a defense (e.g., critical witness is now dead).

Re: how long does the state have to file charges

It depends on the crime.