Generally, the answer to the question of whether a grandparent can seek an order for grandparenting time with their grandchild is that it depends.
Under current Michigan law, in order for a grandparent to seek grandparenting time with their grandchild or grandchildren, one or more of the following conditions should exist: in the case of a married couple, there should be a family law proceeding such as a divorce, separation or annulment which involves the parents of the child pending in court; the parents of the child should have already divorced, separated or have had their marriage annulled; the parent of the minor child with whom the grandparent is seeking grandparenting time is deceased. In the case of an unmarried couple, paternity must have been established. However, if the child has been placed for adoption, then the grandparents' rights terminate.
Once one or more of the conditions above are met then a grandparent who is interested in having a relationship with their grandchild can initiate a court action by filing a motion to seek grandparenting time. The motion should be filed in the Circuit Court for the county the child lives in. Along with the motion, the grandparent must include an affidavit stating the reasons and any other information in support for the motion. Notice of the motion must be given to the parents of the child or the party that has legal custody of the child. Once notice is given to the parties, they may file affidavits opposing the motion. A hearing must be held and at the hearing all parties who have submitted affidavits will have a chance to present their case.
It is very important to keep in mind that if the parents of the child are deemed to be fit parents by the courts, and they deny grandparents time with their grandchild, there is very little a grandparent can legally do. Generally, the legal burden on the grandparent is very high and it must be shown that denying the child time with them results in substantial harm to the child's mental, physical and emotional health.
Source: Michigan Legislature, "Child Custody Act of 1970 §722.27b," Accessed Feb. 16, 2015