Depends on the circumstances that caused the miscarriage. Since the fetus is a person, if the person dies somehow (such as a miscarriage), there could be an investigation into how the person died. If it turns out it's from some action the mother took (such as continuing to drink alcohol through the pregnancy), then the mother is responsible for killing a person. Such is generally considered either manslaughter or homicide.

I don't know how commonly this would be applied if the law passed, but there is precedent for it: Utah apparently has a law defining personhood at some point during the gestation period, and the Melissa Roland was brought up on charges of First Degree Felony Murder for delaying a C-section which lead to the stillbirth of one of her children (the other twin survived). She plead guilty to a lesser charge of Child Endangerment and was convicted of it.

Article on Melissa Roland
Minutes of a Arkansas legislature discussion of a similar bill
YouTube video by Advocates for Pregnant Women w/ more examples from other states w/ similar laws