The Michigan Department of State site notes that if an out of state violation substantially corresponds to a violation of a Michigan law, then the conviction will be posted to your driving record and points will be assessed as required by the Michigan Vehicle Code.

If your ticket had been for a serious offense, not speeding as you received, for which a suspension would have been given if the ticket had been received in Michigan, then a suspension will be imposed after the posting of the violation conviction.

You will need to take care of the Ohio speeding ticket or else your license will likely be suspended in OH and then suspended in Michigan as well. The points assessed to your MI driving record will depend on how many mph over the speed limit you were cited for in Ohio. If 10 mph or less it will be 2 points, 11 to 15 mph over is 3 points and 16 mph or more will result in 4 points on your MI license.