Is there any crime rate information by Census block group available for Michigan state? Possibly in the for of crime count/amount per block group?
Despite my standard hesitation about definitively answering "no" to data-request questions (because it's always possible that it's out there somewhere), I'm going to go ahead and say "no."
Census block groups are not particularly relevant to policing practices, so it's unlikely that any police agencies report data at that granularity. If you're lucky, you might get it at "beat" level. Some places, like Chicago, where I live, offer geocoded crime incident report data which could be mapped to block groups, although Chicago's geocodes are intentionally "blurred" up to about 1/8 of a mile (to preserve privacy) which would make block group aggregates dubious.
Also, depending on how you measure, 70-95% of Michigan is rural, and police jurisdictions in those areas are quite unlikely to report crime data with high geographic precision, for both privacy and data management overhead reasons.
And finally, of course, it bears repeating that crime datasets reflect reported crime, which is inevitably an approximation of real crime, at best. There's not much to be done about that in most cases, but it should temper any analysis and conclusions drawn from crime data.
The only way I'd think you'll get this information is going department by department. While I'd never want to contradict Joe Germuska (and don't have the rep to comment on his reply), any police department with an even sorta-modern computer aided dispatch or records management system will have incident reports with geographic coordinates attached to each incident.
Getting the data from those incident reports depends on a) Michigan's public records' act b) the decency of the individual departments and c) the departments' technical competence.
Once you've gotten the data, it'd be relatively simple to spatially join it with census blocks.
However, getting this for the entire state is almost literally insane. On top of dealing with hundreds of jurisdictions, you'd then have to do some sort of cleaning and standardizing. Updates would be the sort thing that would make you want to shoot yourself. Additionally, crime data is notoriously dirty and it really helps to have some local knowledge before you try to analyze or draw conclusions from any analysis.
TL;DR - no such animal exists for the whole state. You can probably collect the data you need for a town or a county, but doing it for the whole state would be really difficult.
kaggle has some great datasets for all different types of data. Have a look at this dataset. It containts Block, ID of the crime and the coordinates of the indicent.